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Zaitun Time Series English Manual

1. FIGURE 6 Installation Completed Screen 7 You can start using Zaitun Time Series by clicking the shortcut on start menu items Working with Data Creating A New Project Zaitun Time Series represents time series data with the data point frequency annual monthly weekly daily etc ranging from start date to end date To create a new time series data project 1 Click File gt New to open the Create New Project dialog box ER Create New Project Frequency Monthly Observations Tl Project Mare z N ame newproject O00 5 FIGURE 7 Create New Project Dialog 2 Specify the frequency of time series data 3 Set the start date and end date 4 Set the new project name 5 Click the OK button Zaitun Time Series will create a new empty project Zaitun Time Series Lnewp rejet Unsaved Name Type Description FIGURE 8 New Empty Project Opening A Saved Project You can also open a project file saved in your media disk TO open a saved project 1 Click File gt Open to show Open Project dialog Open Series Data Look jr 2 Data shall iF EF fie fas Mi Recent othe Documents Hamiton 2ft E maxtempzft E paper zft cal passenger car miliage data zft passenger ztt ER sossa adjusted mi money zft iy ia sunspot zit iar BS RREAES E Treasury Bill Rates USA January 19620 June 2001 2ft Desktop ira UnemploymentRateLs aft E USconsumer
2. INPUT LAYER FIGURE 106 Architecture of Neural Network Information processing in every neuron is done by summing the multiplication result of connection weights with input data The result is transferred to the next neuron through the activation function There are several kinds of activation functions i e linear semi linear sigmoid bipolar sigmoid and hyperbolic tangent In time series data forecasting the input value for the input layer can be variable data of previous period lagged variable or the other variable used to help forecasting can be qualitative or quantitative To forecast one variable univariate input data for the input layer and output data in the output layer is similar to the autoregressive model AR On certain point of f forecasted data Yu calculated by using P observation Ye Yee Viens from previous point t t l t 2 t n l where shows the number of neuron inputs in a neural network Neural Network Analysis with Zaitun Time Series Zaitun Time Series provides neural network modeling of time series data To perform neural network modeling on a time series variable 1 Click Analysis gt Neural Network gt Trend Analysis Zaitun Time Series sunspot C Program Files Waitun Time Sertes Zaitun Time Series i Decomposition Moving Average o Exponential Smoothing cr 3 Linear Regression Ha Correlogranr ee _ Neuraltietwark
3. Name Description ft il deaths Series deaths paper Series paper pessander Series pessanger sunspot Series FIGURE 107 Neural Network Menu Select Variable Dialog appears Choose a variable you want to build its neural network model and then click OK ce Select Analyzed Variable Analyzed anable deaths paper Passenger Ssunepol FIGURE 108 Select Analyzed Variable Dialog The Neural network analysis form will appear Determine the parameters of the neural network model you want to build You can determine the parameters of the neural network architecture activation function and learning algorithm You can also set up the stopping condition or use early stopping cross validation method ai Neural Network Analysis Form sunspot Neural Network Structure Neurons Count ing Activation Function Stopping Condition input Layer 05 Semi Linear F with Checking Cycle ne a 5 5 Sigmoid Ridden Layer fos p by MSE value Bipolar Sigmoi t ay z 3 Output Layer Hyperbolic Tangent by MSE change Cross Validation Early Stepping E Use Cross Validatian Stopping Progress View 0 Graphic Tex FIGURE 109 Neural Network Analysis Form 4 Click Start The learning process will start and run until the stopping condition is fulfilled or the operation has reached the maximum number of iterations 5 You can stop the learning process any time by clicking Stop while the learnin
4. FIGURE 54 Select Analyzed Variable Dialog 3 The Trend Analysis form will appear Choose the most suitable trend type for the selected variable Trend Analysis passenger Model Type C Linear C Quadratic C Exponential Storage FIGURE 55 Trend Analysis Form 4 To select the analysis result to be viewed on Result View click the Results button Select the result views required by clicking the appropriate checkbox For Forecasted selection enter the data step you wish to forecast ei Select Result View Mile Tables Wna S OK Actual Predicted and Residual Forecasted step 1 2 Cancel Graphics Actual and Predicted Residual Actual and Forecasted C Residual ve Actual Actual ve Predicted Residual vs Predicted FIGURE 56 Select Result View Dialog 5 To save the residual and predicted data of the trend model as a new variable you can click Storage button Check on the item you want to save as a new variable and then type the new variable name Trend Analysis Storage KBI Trend Analysis Storage Options Predicted Cancel Fiesidual ftesid FIGURE 57 Trend Analysis Storage Form 6 After selecting the result views and determining whether you want to save the new variable or not the software will show the Trend Analysis form again Click the OK button to finish your analysis and show the result views 7 The result views selected in previous
5. Save Save 4s Import Export To Excel Lee Te Description FIGURE 35 Export to CSV menu 2 Export to CSV dialog appear Save the CSV file into the directory as you want Export Series Data To MIX Save in i test gt jimage CJ la yimport csy Recent Desktop Mu Documents hy Computer File ame export My Network Save as tine Comma separated File cs FIGURE 36 Export to CSV dialog To export the current Zaitun Time Series project into an Excel file 1 Click File gt Export gt Export to Excel Zaitun Time Series passenger C Program FilesVattun Time SeriesVaitun Ti Open ctri ca Save Ctrl Save Os Import Export ie Export Ta CSV FIGURE 37 Export to Excel menu 2 Export to Excel dialog appear Save the excel file into the directory as you want Export Series Data To Save in O test GF om Sjimage Desktop My Documents bly Computer Filename export w My Network Saveastyper Excel File nls carce FIGURE 38 Export to Excel dialog Importing Data Zaitun Time Series provides a facility to import the data created by another software in a specified format Zaitun Time Series provides a tool to import the data from CSV file csv and Excel file xIs Zaitun Time Series only accept numeric fields both in the Excel format and the CSV format Please do not include non numeric fields e g Nov
6. 876 3360 948 8331 1006 8753 1052 2957 1088 8398 1120 7477 1150 1409 1178 1213 1205 3901 1235 1415 12691287 o n tw we 7 8 nia Project View Variable View Result View Status FIGURE 103 ACF PACF Table 2 ACF Graph Shows the bar chart of ACF values Zaitun Time Series passenger C Program FilesWaitun Time SeriesVaitun Time Series Sample Data passenger zft mE 92 oge yew analysis Toos windows Heip 3x L _ Trend Analysis passenger Decomposition passenger Correlogram Level passenger ACF I PACF f AcF Graph PACF Graph ACF Graph Upper Bound Lower Bound ACF TTT Pret N e CCC Project View Variable View Result view Status FIGURE 104 ACF Graph 3 PACF Graph Shows the bar chart of PACF values Zaitun Time Series passenger C Program FilesWaitun Time SeriesVaitun Time Series Sample Data passenger zft Trend Analysis i passenger Decomposition passenger Correlogram Level passenger ACF PACF ACF Graph PACF Graph PACF Graph Upper Bound lower Bound PACF Project View Variable View Result View Status FIGURE 105 PACF Graph Neural Network Analysis Chapter Neural Network Overview Artificial Neural Network
7. Actual Predicted and Residual Residual vs Actual Graph Residual vs Predicted Graph Project View Variable View Result View Status FIGURE 113 Table of Forecasted 2 Graphics a Actual and Predicted Shows a line plot for actual and predicted values of neural network model b Actual and Forecasted Shows a line plot for actual and forecasted values of neural network model c Actual vs Predicted Shows a scatter plot between actual and predicted values d Residual Shows a line plot for residual values of neural network model e Residual vs Actual Shows a scatter plot between residual and actual values f Residual vs Predicted Shows a scatter plot between residual and predicted values Zaitun Time Series sunspot C Program FilesWaitun Time Serjes Waitun Time Series Sample Data sunspot zft KER a fe ae T T Pam e Rae ee fcg LOSSES Rs __Neural Network sunspot gt Neural Network sunspot Ex w Neural Network Model Summary Actual Predicted and Residual Forecasted f Actual and Predicted Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Actual and Predicted Graph 120 Time Result View FIGURE 114 Actual and Predicted Graph Eek Zaitun Time Series sunspot C Program FilesWaitun Time Se
8. xchange Series Indonesia Exchange Rate From January 20104 to Decemb i FIGURE 12 Added Variable Adding A Group The Zaitun Time Series group represents a collection of several time series variables A group can contain two or more series variables A time series data project can contain more than one group To add a new group into current project 1 Click the Add Group button to open Create New Group dialog te Create New Group ME Name ForeignXChange o vatiables ME Cancel raumas i You car select twa or more variable by pressing Shift or Control key FIGURE 13 Add Group Dialog 2 Determine the new group s name 3 Select variables belonging to this group You can select two or more variables by pressing the Shift or Control key 4 Click the OK button Zaitun Time Series will add this group into current project Zaitun Time Series newproject Unsaved Series USDollarxChange serenge Series Indonesia Exchange Rate from January 2004 to Decemb YenxChange Series YenxXchange FIGURE 14 Added Group Editing A Variable Group You can edit the name or description of a variable group To edit a variable group 1 Select the variable group to be edited Zaitun Time Series newproject Unsaved e a a iS anne eS PES ea ee eee Name Type Description Foreign change Group Group of UsDollarxChange YenkiChange USDollarschange r USDol
9. Double Exponential Smoothing Halt Table Forecasted Actual and Predicted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Actual and Smoothed Graph Actual and Forecasted Graph Actual and Smoothed Graph 14 27 40 53 66 92 105 118 131 144 157 170 183 196 209 Time Project View Variable View Result view Status FIGURE 77 Actual and Smoothed Graph Zaitun Time Series maxtemp C Program FilesWaitun Time Serjes Zaitun Time Series Sample Data maxtemp zft me 7 Double ES Holt maxtemp gt x Exponential Smoothing Model Summary Double EAG Smoothing Holt Table Forecasted Actual and Predicted Graph Actual and Smoothed Graph Actual and Forecasted Graph Residual vs Predicted Graph Residual Graph ALA is l fli hh thy iy WA ih i my Pi ii iy IT Residual ii t 57 71 85 99 113 127 141 155 169 183 197 211 Time Project Yiew Variable View Result View Status FIGURE 78 Residual Graph Decomposition Analysis Decomposition Analysis Overview Decomposition method tries to separate a time series data into several components Decomposition method is often used not only in yielding forecast but also in yielding information about time series component i e trend cycle seasonal and irregular component There are two relation
10. i C H Zaitun Time Series User Manual Content Chapter 1 Introduction 2 Zaitun Time Series 2 Chapter 2 Installation Guide 4 System Requirements 4 Zaitun Time Series Installation 4 Chapter 3 Working with Data 9 Creating A New Project 9 Opening A Saved Project 10 Adding A Variable 11 Adding A Group 12 Editing A Variable Group 13 Duplicating A Variable Group 14 Deleting A Variable Group 16 Viewing A Variable 17 Viewing A Group 22 Transforming A Variable 23 Exporting The Data 24 Importing The Data 25 Adding A Stock Market Data 29 Viewing A Stock Market Data 30 Importing Live Stock Market Data 31 Chapter 4 Trend Analysis 34 Trend Analysis Overview 34 Trend Analysis with Zaitun Time Series 35 Trend Analysis Result 37 Chapter 5 Moving Average Analysis 40 Moving Average Overview 40 Moving Average with Zaitun Time Series 41 Moving Average Analysis Result 44 Chapter 6 Exponential Smoothing Analysis Exponential Smoothing Overview Exponential Smoothing Analysis with Zaitun Time Series Exponential Smoothing Analysis Result Chapter 7 Decomposition Analysis Decomposition Analysis Overview Decomposition Analysis with Zaitun Time Series Decomposition Analysis Result Chapter 8 Linear Regression Analysis Linear Regression Analysis Overview Linear Regression Analysis with Zaitun Time Series Linear Regression Analysis Result Chapter 9 Correlogram Correlogram Overview Correlogram with Zaitun Time Series Correlogram Result View Chapter
11. 2007 in your CSV and Excel file which will be imported to Zaitun Time Series except the first line row which will be the list of variable name of the data To import a CSV file into the current Zaitun Time Series project 1 Click File gt Import gt Import to CSV Zaitun Time Series passenger C Program Files Waitun lime Series VWaitu New Ctrl h Open Ctrl Save Cti 5 Save s Export b Import From Excel Exit Name Type Description FIGURE 39 Import from CSV menu 2 The Open CSV dialog appear Select the CSV file you want to import Import Data FIR Look jrr D tes E Si EP fie Fa import csv Desktop My Documents BE My Computer Ee File name import cs My Network Files of type Comma Separated File csv FIGURE 40 Open CSV File dialog 3 The Import CSV dialog appear The CSV file can t contain non numeric fields except in the first line which will be the variable name Make sure the Use First Row as Variable Name option is checked if your CSV File contains variable name information Then select variables you want to import by making a mark on some check boxes in the variable grid Click the OK button to import the selected variable in the CSV file into the current Zaitun Time Series project Import CSV Sel Imported File FAzaitunsoftware test import csv Options Use First Rowe as Variable
12. The following is the equation of smoothed value S oalY l a Y _ a Y By doing a simple substitution the equation above can be written as S aY l a s Forecasting value Y Forecasting with single exponential smoothing can be done by substituting this equation The equation above also can be written in the following way where e is the forecasting error for n period From this equation we can see that the forecasting resulted with this method is the last forecasted value added with an adjustment for error in the last forecasted value Starting value So Practically to calculate the smoothing statistic at the first observation Y we can use the equation 5 QY 1 a S Then it is substituted into the smoothing statistic equation to calculate S Y l S and the smoothing process is continued until we get S value To calculate the equation above a starting value So is needed So can be calculated from the average of several observations The first several observations can be chosen to determine so Double Exponential Smoothing Browns This smoothing method can be used for data which contains a linear trend This method is often called as Brown s one parameter linear method The following equations are used in double exponential smoothing with Browns method Single smoothing statistic equation Double smoothing statistic equation Forecasting value The proce
13. analyze with moving average analysis and then click OK 3 ER Select Analyzed Variable Analyzed arable paper Cancel FIGURE 62 Select Analyzed Variable Dialog The Moving Average form will appear Choose the moving average method you wish to apply to your variable and set the moving average order ER Moving Average paper Method Single Moving Average gt Double Moving Average OF ancel Moving 4verage Length Ma Length Orde a FIGURE 63 Moving Average form To select the analysis result that will be shown on Result View click the Results button Check the boxes of any number of Result Views you wish to see For the Forecasted selection you have to enter the data step you wish to forecast 5 Moving Average Select Result View Moving Average T able kl el j I FI m Forecasted step 12 Graph Actual and Predicted Residual Actual and Smoothed Residual ve Actual Actual and Forecasted Residual vs Predicted Actual ve Predicted FIGURE 64 Moving Average Select Result View Dialog To save residual predicted or smoothed data from the model as a new variable click the Storage button Check the item you wish to save as a new variable and then type in the new variable name BH Moving Average Storage Form Bic Moving Average Storage Options e __ Smoothed smoothed Cancel Predicted CI Resi
14. 0 5613 12 1899 16 7000 16 5130 1 9075 14 8303 o ll DH ao 18 6000 18 5821 2 0367 18 4205 13 6000 13 2919 1 1020 10 5191 19 5000 19 6119 1 2312 20 6188 24 5000 24 1343 3 5642 20 8431 25 1000 25 3898 1 7773 27 9985 27 0000 27 0167 1 6569 27 1671 23 5000 24 0174 2 0681 28 6737 26 5000 20 6449 3 1116 21 9493 18 2000 18 1333 2 6316 17 5334 14 2000 14 3302 3 5688 15 5017 14 0000 13 6761 1 2370 10 7613 15 6000 15 2839 1 0388 12 4391 Status FIGURE 76 Exponential Smoothing Holt Table 2 Graphics a Actual and Predicted Shows a line plot for actual and predicted values of exponential smoothing model b Actual and Smoothed Shows a line plot for actual and smoothed values of exponential smoothing model c Actual and Forecasted Shows a line plot for actual and forecasted values of exponential smoothing model d Actual vs Predicted Shows a scatter plot between actual and predicted values e Residual Shows a line plot for residual values of exponential smoothing model f Residual vs Actual Shows a scatter plot between residual and actual values g Residual vs Predicted Shows a scatter plot between residual and predicted values Zaitun Time Series maxtemp C Program Files Waitun Time Serjes Zaitun Time Series Sample Data maxtemp zft Double E5 Holt maxtemp SSS Sa S gt xX Exponential Smoothing Model Summary
15. 0000 200 0000 1 6000 275 1745 FIGURE 96 Forcasted Table 6 Residual Graph Shows the plot of residual at time t e and time t Sales C Documents and Settings anas My Documents Sales zft hie Mew Anae Yess Windows Hee file View Analysis Tools Windows Help rT x l Regression Analysis Model 1 Linear Regression Model Summary ANOVA Coefficients Actual Predicted and Residual Forecasted Residual ys Predicted Graph Normal Probability Plot Residual Graph Residual Graph 1995 1997 1999 2001 2003 2005 2007 2009 Time Project vew Variable view pesut View iI Status a em n FIGURE 97 Residual Graph 7 Residual Vs Predicted Graph Shows the plot of residual variable and predicted variable Zaitun Time Series Sales C Documents and Settings anas Wy Documents Sales zft a Bile yew Analysis Tools Windows Help x 7 l Regression Analysis Model 1 z x Linear Regression Model Summary ANOVA Coefficients Actual Predicted and Residual i Forcasted Residual Graph Normal Probability Plot Residual vs Predicted Graph Residual Vs Predicted Graph e Residual Vs Predicted 20 15 Residual 260 Predicted Project view Variable View Result View Status FIGURE 98 Residual Vs Predicted Graph 8 Normal Probability Plot Shows the Normal Probabilit
16. 68 Actual and Smoothed Graph EE 82x Moving Average paper SS i a n Moving Average Model Summary Single Moving Average Table Forecasted Actual and Predicted Graph Actual and Smoothed Graph Actual and Forecasted Graph Actual vs Predicted Graph Predicted Project View Variable View Result View Status FIGURE 69 Actual vs Predicted Graph Exponential Smoothing Chapter Analysis Exponential Smoothing Overview Exponential smoothing is particular type of moving average technique applied to time series data used to produce smoothed data for presentation or to make forecasts The Exponential smoothing method weights past observations by exponentially decreasing weights to forecast future values There are some categories of this method 1 Single exponential smoothing 2 Browns Double exponential smoothing method 3 Holts Double exponential smoothing method and 4 Winters Triple exponential smoothing method Single Exponential Smoothing Single Exponential Smoothing is a procedure that repeats enumeration continually by using the newest data This method can be used if the data is not significantly influenced by trend and seasonal factor To smooth the data with single exponential smoothing requires a parameter called the smoothing constant Each data point is given a certain weighting for the newest data 1 for older data etc The value of must be between O and 1
17. Name pi 358 02 i24 35755 Custom 357 52 rm 367 5 liame 357 41 USEechangeh ate Ir fenExchangeHate 355 78 l l 338 02 USConsumerindex 337 477 328 75 320 07 Fla 72 305 13 30254 303 56 FIGURE 41 Import CSV dialog To import an Excel file into the current Zaitun Time Series project 1 Click File gt Import gt Import to CSV C Program FilesVaitun Time SeriesVaitun lime Zaitun Time Series passenger Tools hds iiep a ateh bei r pen Ctrleo Save Cti sS Save s E Export __Import From Excel Arey eee pag 1 na a Jo E I MN 1 Ed a ATA aE Exit i Name Type Description FIGURE 42 Import from Excel menu 2 Open Excel dialog appear Select the Excel file you want to import Import Data Look jr gt test Ted ijirage Cd Ei import xiz Recent Desktop My Documents bio Computer Filename import pals Mii Network Files of type Excel Files sl FIGURE 43 Open Excel File dialog Import Excel File dialog appear The Excel file can t contains non numeric field except the first row which will be the variable name Make sure the Use First Row as Variable Name option is checked if your Excel File contains variable name information Then select variables you want to import by making a mark on some check boxes in the variable grid You can switch between sheets by selecting t
18. Next to continue or Cancel to exit the Setup Wizard WARNING This progrannis protected by copyright law and international treaties J c R T U Freeware FIGURE 1 Welcome Screen 3 Read the license agreement and then click I accept the terms in the License Agreement to continue installing Zaitun Time Series ie Zaitun Time Series License Agreement End User License aircon Please read the following license agreement carefully 9 Zaitun Time Series is a free and open source program released under GPL v3 You can use itfor any purpose include for commercial use This Software is provided asis withoutwarranty ofany kind either expressed or implied Please consider to donate Us Ifyou find this software ls useful for you ar your work twill hel us to continue Zaitun Time Series development kaa 1 nir mi 1 F ioa me Aan OO i fa accept the terms In the License Agreement Installer2a0 Freeware seak u FIGURE 2 End User License Agreement Screen 4 Choose Destination Location Screen appears You can choose to install Zaitun Time Series into the default directory C Program Files Zaitun Time Series or choose another directory If you want to change the destination location of Zaitun Time Series click Browse button Click Next button to install into default directory iz Zaitun Time Series setup Choose Destination Location Select the Folder you would like Setup to ins
19. Series Sample Data sunspot zft aAA Spreadsheet sunspot deaths sunspot Project View Yarlable View Result View FIGURE 29 Graphic View Statistics View shows simple descriptive statistics of a variable making it easy for you to analyze statistical properties of a variable Zaitun Time Series sunspot C Program FilesWaitun Time Serie sunspot deaths Descriptive Statistics for Variable sunspot Descriptive Statistics 12134 9 46 0529 36 5 14 5 66 6 3528526 1473 428 0 6528205 a 9154359 FIGURE 30 Statistics View Viewing A Group Zaitun Time Series provides two ways to view a group spreadsheet view and graphic view Viewing a group is not so different from viewing a variable Just by double clicking the group you want to view Zaitun Time Series will switch the main pane to Variable View and the selected group Zaitun Time Series 4m6m C Program Files aitun Time Series GS56M Pr oject View Variable View Result View Status FIGURE 32 Graphic View of A Group Transforming A Variable Zaitun Time Series provides several transformation types that can be applied to a variable They are differencing seasonal differencing logarithm and square root To transform a variable 1 Click Tools gt Transform Variable to show Transform Variable dialog T
20. of four members who work hardly in developing Zaitun Time Seiries The members of the team are Rizal Zaini Ahmad Fathony the founder and core programmer of Zaitun Time Series Suryono Hadi Wibowo as programmer and GUI designer Khaerul Anas as programmer and Lia Amelia as documentation and administrator of Zaitun Time Series website Zaitun Time Series is freeware It can be used for any purpose including commercial use This software is provided as is without warranty of any kind either expressed or implied Zaitun Time Series copyright 2007 2010 zaitunsoftware com All Rights Reserved Installation Guide System Requirements Minimum Requirements e Windows XP SP2 or later Windows Vista Windows 2000 SP4 or later or Windows Server 2003 SP1 or later e NET Framework 2 0 e 600 MHz processor Recommended 1 GHz or faster e 192 MB of RAM Recommended 256 MB or more e 1024 x 768 screen resolution e 10 MB hard drive space Zaitun Time Series Installation Zaitun Time Series installation is very simple and only takes a few minutes To install Zaitun Time Series 1 Please ensure that NET Framework 2 0 is installed in your system 2 Start zaitun msi It will install Zaitun Time Series into your computer The welcome screen appears Click Next iz Zaitun Time Series setup Welcome to the Zaitun Time Series Setup Wizard The Setup Wizard will install Zaitun Time Series on your computer Click
21. you click Yes on the confirmation dialog then the selected variable group will be deleted from the current project R Zaitun Time Series newproject Unsaved Tools windows Name Tepe PARARON m Foreign change Group Group oF USCollarschange Yenxichange Indonesiansichange Series Indonesia Exchange Rate from January 2004 to Decemb USDollar change Series UsDollarsChange Yenk Change Series Yensichange FIGURE 23 Data View Screen after Deleting a Variable Viewing A Variable Zaitun Time Series provides three ways to view a variable spreadsheet view graphic view and statistics view Viewing a variable is very simple Double click the variable you wish to view Zaitun Time Series will switch the main pane to the Variable View and view the selected variable Zaitun Time Series newproject Unsaved le des eS dows Help E P January 2004 March 2004 April 2004 May 2004 June 2004 FIGURE 24 Variable View You can also view a variable by manually switching the main pane to the Variable View Pane and clicking Add Pane button on the top left side of the Variable Pane Select Variable dialog appears Select the variable you want to view and then click OK Zaitun Time Series will add a new pane on the Variable Pane to view the variable Project view Variable View Result wiew Status FIGURE 25 Variable View Pane E Select VariablefGr
22. 00 127 8694 119 9673 157 7456 9 7486 148 0000 129 1315 122 5338 155 9659 7 9689 136 0000 130 4299 128 2073 138 3577 2 3577 119 0000 131 7643 128 8205 121 7194 2 7194 104 0000 133 1344 129 3746 107 0224 3 0224 118 0000 134 5396 130 3960 121 7497 3 7497 115 0000 135 9795 126 3842 123 7310 8 7310 126 0000 137 4539 143 1625 120 9758 5 0242 141 0000 138 9622 140 0492 139 9057 1 0943 135 0000 140 5042 138 5101 136 9435 1 9435 125 0000 142 0792 127 9447 138 8092 13 8092 149 0000 143 6871 133 4319 160 4517 11 4517 170 0000 145 3273 137 8003 179 2858 9 2858 Projest View Variable View Result View Status FIGURE 84 Decomposition Table 2 Graphics a Actual Predicted and Trend Shows a line plot for actual predicted and trend values of decomposition model b Actual and Forecasted Shows a line plot for actual and forecasted values of decomposition model c Actual vs Predicted Shows a scatter plot between actual and predicted values d Residual Shows a line plot for residual values of decomposition model e Residual vs Actual Shows a scatter plot between residual and actual values f Residual vs Predicted Shows a scatter plot between residual and predicted values g Detrended Graph Shows a line plot for detrended values of decomposition model h Deseasonalized Graph Shows a line plot for deseasonali
23. 10 Neural Network Analysis Neural Network Overview Neural Network Analysis with Zaitun Time Series Neural Network Modeling Result 47 47 51 54 57 57 57 60 63 63 66 68 72 72 73 75 77 77 78 82 Zaitun Time Series User Manual Zaitun Software Developer Team www zaitunsoftware com Introduction Zaitun Time Series Zaitun Time Series is designed for ease of use for statistical analysis series modeling and forecasting of time series data It provides several statistics and neural networks models and graphical tools that will make your work on time series analysis easier Statistics and Neural Networks Analysis O Trend Analysis O Decomposition O Moving Average O Exponential Smoothing O Linear Regression O Correlogram O Neural Networks Graphical Tools O Time Series Plot O Actual and Predicted Plot O Actual and Forecasted Plot O Actual vs Predicted Plot O Residual Plot O Residual vs Actual Plot O Residual vs Predicted Plot O Normal Probability Plot Zaitun Time Series was originally developed by the Time Series team as the final project of their four years diploma degrees in Sekolah Tinggi Ilmu Statistik Jakarta Indonesia Members of the team are Rizal Zaini Ahmad Fathony Suryono Hadi Wibowo Wawan Kurniawan Muhamad Fuad Hasan Al Maratul Sholihah and Rismawaty Now the developer team in zaitunsoftware com is continuing the development of Zaitun Time Series The developer team now consists
24. 94766 0 82332 856017 8 64350 874213 3 07778 3 24963 9 57428 10 20119 071215 0 84800 Select This Cancel FIGURE 73 Double ES Holt Grid Search 5 To select analysis result that will be shown on Result View click Results button You can select some result views by clicking the checkbox of every selection For Forecasted selection you have to enter the data step you wish to forecast Exponential Smoothing Select Result View Tabel yi i l Lar Tlie Exponential Smoothing Table Smoothed Trend ii ri ICTUS f F EFi Forecasted Grafik 7 Actual aid Predicted Actual ard Smoothed Actual and Forecasted Actual ve Predicted Cancel aea step li 2 Residual Redidual ve Actual Residual v Predicted FIGURE 74 Exponential Smoothing Select Result View 6 To save the residual predicted or smoothed data from the model as a new variable click the Storage button Check the items you want to save as new variables and then type the new variable names Exponential Smoothing Storage Form KBI Exponential Smonthing Storage 0 piore a v Smoothed smoothed Cancel Predicted Residual FIGURE 75 Exponential Smoothing Storage Form 7 After selecting the result views and determining whether you want to save the new variables or not the software will show the Exponential Smoothing form again Click the OK button to finish your analysi
25. P 0 j 1 2 p l 2 Test Statistic We can use F statistic and ANOVA table Source of Sum Degree of Mean Squares Fabs Variation Squares Freedom Regression MSR SSR p 1 MSR MSE Error MSE SSE n p Ld Total Where Sol ry J Square matrix withall elements 1 SSE e e Y Y BX Y SSR SST SSE 3 Decision We reject Ho if Pons gt Facp n p 4 Conclusion If Ho is rejected means that there is at least one of predictor has linear relationship with dependent variable Testing Partially Partial Test 1 Hypothesis H Pp 0 H Pp 0 2 Test Statistic where se B X X MSE 3 Decission obs We reject Ho if fos gt farzin p or Fors lt Faian p 4 Conclusion If 1 is rejected means that there is effect of independent variable to dependent variable We can compute confidence interval of regression coefficients of l using equation tipga p For measuring proportionate reduction of total variation in Y associated with the use of set of X variables we can use the coefficient of determination R that is defined as follows _SSR_ SSE SST SST The correlation coefficient R describe of degree of the linear relationship between independent variables and dependent variable is defined as Square root of R R VR where 1SR lt 1 Usually by adding more of predictor can increase the value of R On other hand it can be more complicated in interpreta
26. PriceIndex zt 3 its UsexchangeRate 2ft ial WenExchange zFt My Computer 5 a Filename ee J b y Network Files of type zaltimeFiles 2A we zaftime Files att FIGURE 9 Open File Dialog 2 Specify your project file location zft file 3 Click the Open button Zaitun Time Series will open the selected project file Zaitun Time Series sunspot C Program FilesWaitun Time Serjies Vaitun Tim Name Type Description deaths Series deaths paper Series paper pessanger Series pessanger sunspot Series FIGURE 10 Opened Project File Adding A Variable A Zaitun Time Series variable is a series of data points constituting one time series data collection For example the recorded annual monthly weekly daily time series values of the Indonesian Exchange Rate A time series data project can contain more than one variable To add a new variable into current project 1 Click the Add Variable button on top left side of current project view to open Create New Variable dialog ie Crete New Variable TEN change Indonesia Exchange Rate from Janda 1980 ta Pecember 2006 FIGURE 11 Create New Variable Dialog 2 Determine the new variable s name and its description 3 Click the OK button Zaitun Time Series will add this variable into current project Zaitun Time Series newproject Unsaved O gle Wew Analysis Toos Windows Help zki Name Type Description
27. Values button Enter the test value for each predictors as many as the step you set and then click OK Set Values Promotion competitor 6 19 FIGURE 9O Set Values Dialog 5 Click OK the Select Result View Dialog and click the Storage button to save the value of predicted and residual variable Determine the variable s name and then clik OK SR Linear Regression Storage Qphons 7 Predicted PredSales 000 e Residual ResSaef OO OOOO FIGURE 91 Linear Regression Storage Form 6 Click OK button on the Linear Regression Analysis Dialog to run analysis Linear Regression Analysis Result The result views of Linear Regression Analysis in Zaitun Time Series are 1 Linear Regression Model Summary Shows analyzed variables model type number of observation regression equation R R AdjR standard error and durbin watson Statistic Zaitun Time Series Sales C Documents and Settings anas My Documents Sales zft aie ee analysis Tools Windows Help hrs Regression Analysis Model 1 l Linear Regression Model Summary ANOVA Coefficients Actual Predicted and Residual Forecasted ResidualGraph Residual vs Pr Linear Regression Model Summary Model Summary gt Variable Dependent Predictors Costant Promotion competitor Outlet PopulationGrowth Model Type Multiple Linear Regression Included Observation 15 Regression Equation Sales 51 2750 1 9596 Pro
28. Windows Help _ x ERSA G Trend Analysis passenger Trend Analysis Model Summary Actual Predicted and Residual Forecasted Actual and Predicted Graph Actual and Forecasted Graph ActualvsPredictedGraph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Actual Predicted Residual 1 112 0000 93 1561 18 8439 2 118 0000 95 7526 22 2474 3 132 0000 98 3491 33 6509 4 129 0000 100 9456 28 0544 5 121 0000 103 5421 17 4579 6 135 0000 106 1386 28 8614 sZ 148 0000 108 7351 39 2649 8 148 0000 111 3316 36 6684 9 136 0000 113 9281 22 0719 119 0000 116 5246 2 4754 104 0000 119 1211 15 1211 116 0000 121 7177 ooo 3 7177 115 0000 124 3142 9 3142 126 0000 126 9107 0 9107 141 0000 129 5072 11 4928 135 0000 132 1037 2 8963 125 0000 134 7002 9 7002 149 0000 137 2967 11 7033 9 170 0000 139 8922 30 1068 Project View Variable View Result View Status pau o E na aaeeea rrr FIGURE 59 Table of Actual Predicted and Residual Value 2 Graphic a Actual and Predicted Shows the line plot for actual and predicted values of trend model b Actual and Forecasted Shows the line plot for actual and forecasted values of trend model c Actual vs Predicted Shows the scatter plot between actual and predicted values d Residual Shows the line plot for residual values of trend model e Residual
29. as independent variables This equation constant is a starting value estimation for o and slope of regression coefficient is a starting value estimation for the trend component To Whereas the starting value for the seasonal component Sa is calculated by using dummy variable regression on detrended data without trend Exponential Smoothing Analysis with Zaitun Time Series Zaitun Time Series performs exponential smoothing analysis of time series data including single exponential smoothing double exponential smoothing Browns double exponential smoothing Holts and triple exponential smoothing Winters To perform exponential smoothing analysis on a time series variable 1 Click Analysis gt Exponential Smoothing Zaitun Time Series maxtemp C Program FilesWaitun Time Serjes Vaitun Time Correloaranr 3 gt Neuralvetwork maxtemp FIGURE 70O Exponential Smoothing Menu 2 Select Variable Dialog appears Choose a variable you want to analyze with exponential smoothing analysis and then click OK H bey Select Analyzed Variable Analyzed anable Cancel FIGURE 71 Select Analyzed Variable Dialog 3 The Exponential Smoothing form will appear Choose the Exponential Smoothing method you want to apply to your variable and determine the smoothing constant alpha beta and gamma For Triple Exponential Smoothing determine its type multiplicative or additive a
30. at the stock market Low Variable is a variable which shows the lowest value of shares at certain period at stock market Volume Variable is a variable which shows the volume of transactions in a particular period The feature of add stock market data in Zaitun Time Series is only available on project with Daily5 Weekly and Monthly frequency To add a new stock market data in the current Zaitun Time Series project 1 Click Add Stock button on the top at the current project view on project group s button to open Create New Stock dialog Nae Stock Desenption MyStack Li ta Venables Stack Variabhes Open ise Operar High C Higa Low E Close CI lessa Volume L lt VolumeMar FIGURE 45 Create New Stock Dialog 2 Determine the new stock s name the description and stock s variables from the list of variables 3 Click OK button Zaitun Time Series will add this stock into the current project Zaitun Time Series StockExchange C Program FilesVaitun Time SeriesVaitun Time ie oe Name _Type Description Closevar Series Those var High ar Series High ar Low ar Series Low var PreSback Starck MarShoch Open ar Series pen var Volumevar Series Volurmevar FIGURE 46 Added Stock Viewing A Stock Market Data Zaitun Time Series provides two ways to view a stock market data spreadsheet view and graphic view Viewing a stock market data is very simple like viewin
31. cast T Y T 1 Y T 2 Y Double Moving Average This method is based on the calculation of the second moving average The Second moving average is calculated from the average of first moving average notated by MA T x T means MA T period from MA T period This method can be used to forecast data with a linear trend component The procedure to calculate double moving average is Farr aa T 2 Calculate adjustment which is the difference between single MA and S 4S 7 T 3 Adjust trend from period n to n m if you want to forecast m period ahead 1 Calculate single moving average S double MA S S where S The forecasting value for m period ahead is a where it is the adjusted average value for period n added by the value of multiplication between m and trend component b Moving Average Analysis with Zaitun Time Series Zaitun Time Series provides a feature to perform moving average analysis of a time series Single moving average and double moving average are available To perform the moving average analysis on a time series variable 1 Click Analysis gt Moving Average Zaitun Time Series paper C Program Files Vaitun Time SeriesVattun Ti lt Moving Average iS Exponential Smoothing Linear Regression j paaa Correlogranr 3 Neuralvetwork Series FIGURE 61 Moving Average Menu 2 Select Variable Dialog appears Choose a variable you want to
32. d FIGURE 65 Moving Average Storage Form After selecting result views and determining whether you want to save the new variable or not the software will show the Moving Average form again Click the OK button to finish your analysis and to show the result views The result views selected on the previous step will be viewed as several tabs on the Result View panel Moving Average Analysis Result The result views of moving average analysis in Zaitun Time Series are grouped into two categories they are tables and graphics The details of them are described here 1 Tables a Model Summary Shows the summary of moving average model b Moving Average Table Shows actual MA predicted and residual values of moving average model c Forecasted Shows forecasted values from moving average model as many steps of data you want to forecast Zaitun Time Series Beta Edition paper C Program Files Aleebra Zaitun Time Series Sample Data paper zft Moving Average paper z x Moving Average Model Summary Single Moving Average Table Forecasted Actual and Predicted Graph Actual and Smoothed Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Moving Average Model Summary for paper Model Summary b Variable Model Included Observation Accuracy Measures Mean Absolute Error MAE 10 126389 Sum Square Err
33. d In several cases linear trend is not suitable for time series data These cases occur when a time series has a different gradient between the beginning phase of the data and the next phase For these cases it is better to use nonlinear trend than linear trend There are several nonlinear trends they are Exponential Tr ab Quadratic Tr a bY cY Cubic Te at bY cY dY The most suitable trend is a one with the smallest error that is the smallest difference between actual data and estimated data from trend value The common rule used to find the best trend is by choosing a trend with the smallest standard error value and having the biggest R square value Trend Analysis with Zaitun Time Series Zaitun Time Series provides a feature to analyze trend component of a time series There are several trend types available e g linear quadratic cubic and exponential To make a trend analysis of a time series variable 1 Click Analysis gt Trend Analysis menu a C Decomposition Moving Average I Exponential Smoothing 4 Linear Regression Period dp Correlogranr Neuralnetwork Name The DeEcription FIGURE 53 Trend Analysis Menu 2 The Select Analyzed Variable Dialog appears Choose a variable you want to analyze with trend analysis and then click OK ce Select Analyzed Variable EE Analyzed arable Paper Passenger Se surspol Cancel
34. dure to calculate forecasting m forward period with double exponential smoothing with Brown method can be calculated from this equation This equation is similar to linear trend method where Starting value So The smoothing statistic equation above can be solved if the estimation value for o is defined Starting value So is defined as A Q a So Poo ee NEN A a AW So Poo ee Pio a We can use linear trend model constant calculated with the least square estimation method to estimate the coefficient of So Povo and Bro Double Exponential Smoothing Holts This method is similar to Browns method but Holts Method uses different parameters than the one used in original series to smooth the trend value The prediction of exponential smoothing can be obtained by using two smoothing constants with values between O and 1 and three equations as follows S aY l a S _ T 1 S 7 m 3 Equation 1 calculates smoothing value S from the trend of the previous period l added by the last smoothing value ee Equation 2 calculates trend value T from na Sia and Jn Finally equation 3 forward prediction is obtained from trend Le multiplied with the amount of next period forecasted m and added to basic value Mia Starting Value o and 1o There are two parameters needed to estimate exponential smoothing with Holts method the smoothing value So and the trend To To find these parameters the l
35. e series data is stationary or not you can use the statistical test based on standard error se By following the normal distribution standard the interval with signification equal to 95 for Px with the sample number equal to T is Ph 1 96 x se or p 1 96x V If ACF coefficient value is in interval with signification equal to 95 then null hypothetic Ho that shows ACF value k equal to O can not be rejected It means that the data is stationary Besides that to know whether time series data is stationary or not Q statistical test which follows Chi Square distribution can be used Q statistical value formulated below Qn n n ng 2 Where m Number of the tested lag Q Q statistical value in lag m n The number of samples Py ACF coefficient in lag k If the Q statistical value is smaller than Q value obtained from chi squares z table in certain significant level then null hypothetic Ho which shows that ACF value Pk equal to O can not be rejected It shows that the data is stationary Corellogram with Zaitun Time Series Zaitun Time Series displays the autocorrelation function ACF values and graphic of a time series To display corellogram of a time series variable 1 Click Analysis gt Corellogram Zaitun Time Series passenger C Program Files Waitun Time SeriesVaitun Time Series Sa Analysis Tools Windows Help Trend Analysis Decomposition Moving Av
36. east squares method is used The estimation value for So is the intercept value of linear estimation while lo is the Slope value Triple Exponential Smoothing Winters If a time series is stationary the moving average method or single exponential smoothing can be used to analyze it If a time series data has a trend component then double exponential smoothing with Holts method can be used However if the time series data contains a seasonal component then the Triple Exponential Smoothing Winters method can be used to handle it This method is based on three smoothing equations Stationary Component Trend and Seasonal Both Seasonal component and Trend can be additive or multiplicative Additive The whole smoothing equation u aly S _ l a a T Trend smoothing EW Sy is Seasonal smoothing Forecasted value Multiplicative The whole smoothing equation Yn a LL 5 1 g aM L n l Trend smoothing T Wu l 1 YT Seasonal smoothing s B 1 A s n Forecasted value AN YY u T m S n l m Where is seasonal length for example amount of month or quartile in a year T is trend component S is seasonal adjustment factor and Yi n is forecasted value for m next period Starting value 0 T and The starting values for o and l can be obtained from regression equations which have actual variables as dependent variables and time variables
37. erage Exponential Smoothing Linear Regression Neuralvetwork Name Te e Dee cription ae dpassenger Series DiFferencing transformation From passenger passenger Series trendi Series Trend Value of Decomposition Classic analysis of variable FIGURE 100 Correlogram Menu 2 Select Variable Dialog appears Choose a variable for the corellogram which you wish to display and then click OK ER Select Analyzed Variable Analyzed anable dpassenger passenger trend rr waa ii l Cancel FIGURE 101 Deseasonal Graph 3 The Correlogram form will appear Select the data you wish to display original data level first differencing data or second differencing data Also determine the number of the included lag Click OK to display the result Comelogram of Level C tat difference CK C 2nd difference Number of Lage Number of lags 32 FIGURE 102 Correlogram Form 4 The Corellogram result will be viewed on the Result View panel in several tabs Corellogram Result View The result views of correlogram in Zaitun Time Series are 1 ACF PACF Table Shows ACF PACF Q statistics and probability values Zaitun Time Series Beta Edition passenger D data skripsi passenper zft Correlogram Level passenger ACF PACF ACF Graph PACF Graph ACF 216 0251 295 9567 363 3282 424 6205 482 1336 537 7338 592 3897 651 4181 arra 793 9558
38. g a variable Double click the stock data you wish to view on Project View or by clicking Add Pane button on the top of Variable Pane Zaitun Time Series will view the selected stock data Zaitun Ti ies StockExchange C Program FilesWaitun Time SeriesWaitun Time Series ay ied ace ols vindoy iS X ols SS ES 5 MyStock Beh iais February 2009 March 2009 April 2009 May 2008 June 2009 July 2009 August 2009 September 2009 October 2009 November 2009 December 2009 FIGURE 47 Spreadsheet View The Spreadsheet View is the default view and you can show the Graphic View by clicking the Grapic button on the top of the Variable View Zaitun Time Series msft Unsaved baa a File View Analysis Tools Windows Help joo 8 y htt tere pitied PAP PII Palea li a wen bt he gh Tane a TULNU a rie 13 10 09 05 11 09 30 11 09 23 12 09 FIGURE 48 Graphic View Importing Live Stock Market Data Zaitun Time Series has a feature to import a live stock market data from online stock data provider such as Yahoo Finance This feature is very useful especially for people who have an intensive interaction with the stock market in order to analyze the market or trade the market They can easily import the stock market data from online data provider to Zaitun Time Series and then choose the right method available in Zaitun Time Series to make a p
39. g process is running a Neural Network Structure Neurons Count ing Activation Function Stopping Condition hint Layer Semi Linear E with Checking Cycle 100 S DO Sigmoid Bipolar Sigmoid Hyperbolic Tangent Hidden Layer Output Layer Cross Validation Eary Stopping Use Crogs Validatian Stopping Generalization Loss Treshold 7 9 Leaming Eror 1075443 Generalization Loss 2 00575 Validation Set Ratio 0 2 PQ Treshold 15 Strip gp n E Stas FO ekza Progress View 0 Graphic O Ted None Actual Predicted 1398 Eror 096128 MAE 295761 MSE 169 40003 FIGURE 110 The Result of Neural Network Analysis Form 6 After the learning process is finished click the View Result button to display the model result E Select Result View Tables AM yell Sere a i agi F Forecasted eo Graphics Actual and Predicted Residual Actual and Forecasted Residual ve Actual Actual vs Predicted Iv Residual vs Predicted FIGURE 111 Select Result View Ti 8 The Select Result View dialog will appear Select the result views you want to display and then click OK You can forecast the data by clicking the Forecasted item and determine the number of data you want to forecast The selected model result will be displayed on Result View panel in several tabs Neural Network Modeling Result The result views of neural network modeling in Zaitun Time Series are grouped into two categories tables and gra
40. he sheet combo box in the Preview Pane Click OK button to import the selected variable in Excel file into the current Zaitun Time Series project i Import Excel File GEES Imported File FPAzaitunsoftwarestest import sls OK Cancel Optrione Freie Use First Rows as Sheet ERE Vanable Name a Custom Colur Columna Colurnin A No Name A 1 USExchargeRate Jeee EREE VenExchangeRate USConeumerndex 261 3a02 C Jas i k 261 357 55 Jate USCons melndes a VEz Se Er 3575 22 245 357 41 Ze 244 387 41 221 23 3574 222 335 355 78 Taa 234 338 02 J224 fenExchangeR ate FIGURE 44 Import Excel File Dialog 4 Click the OK button Zaitun Time Series will add this variable into current project Adding Stock Market Data Zaitun Time Series provides a facility to help the user to view their stock market data easily with spreadsheet view and graphic view with a candlestick graph which helps the user to analyze the movement of their stock market data esily A Stock market data in Zaitun Time Series consists of five variables they are Open Variable High Variable Low Variable Close Variable and Volume Variable Open Variable is a variable which shows a value of shares at the stock market opening Close Variable is a variable which shows a value of Shares at the stock market closing High Variable is a variable which shows the highest value of shares at certain period
41. l Predicted and Residual Table Shows the value of actual predicted and residual variable Zaitun Time Series Sales 16 6504 C Documents and Settings anasWy Documents 254 0000 Regression Analysis Model 1 Linear Regression Model Summary ANOVA Predicted Actual gt 1995 206 0000 212 2150 218 4575 254 9304 Residual Coefficients 7 2150 12 4575 0 9304 246 0000 236 8717 9 1283 201 0000 291 0000 234 0000 j 209 0000 204 0000 195 0917 292 3872 233 9191 214 1222 199 7260 5 9083 1 3872 0 0809 5 1222 4 2740 216 0000 230 1446 14 1446 245 0000 239 7725 5 2275 286 0000 279 7350 6 2650 312 0000 324 2638 12 2638 265 0000 322 0000 FIGURE 95 246 3989 315 9643 16 6011 6 0357 22 7197 Actual Predicted and Residual Table 5 Forcasted Table Shows the value of forcasted of dependent variable Zaitun Time Series Sales C Documents and Settings anas WMy Documents Sales zft mE G ete Wien 3 Bree ere Task Ll File Wew Analysis Tools il Ele Mew Analysis SoS SSNS Fz SZ Regression Analysis Model 1 Linear Regression Model Summary ANOVA Coefficients Actual Predicted and Residual Forcasted competitor Sales Promotion Outlet 5 0000 19
42. l trend models available linear quadratic cubic and exponential EE Decomposition passenger Seazonal Length Seasonal Length i Model Type Multiplicative O Additive Trend Trend Model Baris FIGURE 81 Decomposition Form 4 To select the analysis result that will be shown on Result View click the Results button Select the required result views by clicking the appropriate checkbox For Forecasted selection you have to enter the step of data you want to forecast Decomposition Select Result View Decomposition Table Trend Detrended Seasonal Seasonal adj sted EES Forecasted step 2 Gratik Actual Predicted and Trend Detrend Actual and Forecasted Seasonal adjusted Actual v Predicted Residual v2 Actual Residual Residual ve Predicted FIGURE 82 Decomposition Select Result View 5 To save trend detrended deseasonalized residual or predicted data from the model as new variables click the Storage button Check the item you want to save as a new variable and then type the new variable name Decomposition Storage Form ole Decomposition 5 torage Ophons Trend tend Cancel Detrended Deteasonalized Predicted C Residual FIGURE 83 Decomposition Storage Form 6 After selecting result views and determining whether you want to Save the new variables or not the software will show the Decomposition form again C
43. larkChange Indonesia Exchange Rate trom January 2004 to Decemb Venschange Series Venschange FIGURE 15 Selected Variable 2 Click the Edit button to show the Edit dialog H Edit Variable Name Indonesi herse Description Indonesia Exchange F Exchange Rate from January 19801 anwar 1980 ta Cancel December 2006 FIGURE 16 Edit Variable Dialog 3 Edit the name or description of this variable and then click the OK button Zaitun Time Series newproject Unsaved Srp ges pet oe Wire oe Oras TPC Heg Dra CERS E AS O NEAT Name Type Description Foreign Change Group of USDollarachange venachange Indonesian hange Indonesia Exchange Rate trom January 2004 to Decemb UsDollar Change Series USDollarschange YenxChange Series Yensichange FIGURE 17 Edited Variable Duplicating A Variable Group You can duplicate a variable group A duplicated variable group has the same value as its source To duplicate a variable group 1 Select the variable group you want to duplicate Name Type Description Foreign change Sroup Group oF USDollartChange Yenktichange Indonesian change Series Indonesia Exchange Rate from January 2004 to Decemb USDollarkchange Series USDollarktchange FIGURE 18 Selected Variable 2 Click the Duplicate button to show the Duplicate dialog t Duplicate Variable YenXChange KES New Variable Name Lk j FIGURE 19 Duplica
44. les the dependent variable from independent predictor variables such as promotion competitor outlet and population growth After developing the model this method can forcast the value of the dependent variable for the given test values of independent variables In practice regression model with one predictor is rarely used in research Frequently many researchers use more than one predictor The general purpose of multiple linear regression is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable Formally the model for multiple linear regression given n observations is YEP tPA at Py tar Pe Pes tH LZ Where Y Dependent variable X Independent variable predictor p Regression parameter E Error P number of parameter n number of observation We can also denote the multiple linear regression in matrix form as below Y Xp eE Where Y l Xa X X1 p 1 p E y l Xa Xn tt Xa p Y 7 X 2 2 a B e 2 Ya l Xna na Anpa p E Using Ordinary Least Square OLS method we can compute estimator of parameters by equation B X X X Y estimator of Y by equation Y xB and vector of residual Y Y Before analyzing the regression model we have to test of significance of the regression coefficients simultantly and partially Testing Simultaneously Overall Test 1 Hypothesis Hy P 6 6 4 9 H There is atleast one of
45. lick the OK button to finish the analysis and to show the result views 7 The selected result views from the previous step will be viewed as several tabs on the Result View panel Decomposition Analysis Result The result views of decomposition analysis in Zaitun Time Series are grouped into two categories they are tables and graphics The details of them are described here 1 Tables a Model Summary Shows the summary of decomposition model b Decomposition Table Shows actual smoothed trend seasonal predicted and residual values of decomposition model c Forecasted Shows forecasted values from decomposition model as many steps of data you want to forecast Zaitun Time Series Beta Edition p assenpger ctx lini Aaka Fk ine ie VIEW Analysis Tools uy Os D data skripsi passenper zft Bec tile 8 xX Forecasted Actual Predicted and Trend Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Detrend Graph Deseasonal Graph Detrended Seasonal Deseasonalized Predicted Residual 121 0839 123 0872 110 1771 1 5229 118 0000 1221192 134 0728 107 4794 10 5206 132 0000 123 1932 131 1099 124 0295 7 9705 129 0000 124 3056 132 3541 121 1555 7 8445 121 0000 125 4561 123 8505 122 5687 1 5687 135 0000 126 6442 120 8946 141 4203 6 4203 148 00
46. motion 1 0840 competitor 0 5513 Outlet 3 0347 PopulationGrawth R 0 9764 R Square lo 9534 R Sguare Adjusted 0 9348 Standard Error of Estimates 10 4969 Durbin Wwatson 2 2202 FIGURE 92 Linear Regression Model Summary 2 ANOVA Table Shows value of MSR MSE Fops and significance IND Regression Analysis Model 1 Linear Regression Model Summary ANOVA Coefficients Actual Predicted and Resic Mean Square 4 df F Sig 5640 4370 51 1905 0 0000 1101 5522 o 110 1852 23663 6000 14 FIGURE 93 ANOVA Table 3 Coefficients Table Shows the value of parameter B se B statistic t significance A confidence interval of VIF z order correlation and partial correlation H Zaitun Time Seri s Sales C Documents and Settings anas Wy Documents Sales zft gt Constant Promotion competitor Outlet PopulationGrowth Regression Analysis Model 1 Linear Regression Model Summary ANOVA Coefficients aneeanesesesenssesssenecessos es 33 3926 1 5355 0 7968 1 8553 0 9843 0 1169 4 7170 j 2 4592 _ Sig 95 CI for B Upper Bound of 95 CI for B 125 6784 3 7350 5 2178 o 8118 VIF Actual Predicted and Residual Forecasted Residual Graph Residual vs Predicted Graph Normal Probab Z Order Correlation 8 8347 10 3435 FIGURE 94 Coefficients Table 4 Actua
47. nd seasonal length i Exponential Smoothing maxtemp Method Modal Type Single Exponential Smoothing C Double Exponential Smoothing Brown C Double Exponential Smoothing Halt Seasonal Length C3 Triple Exponential Smoothing Winter Smacthing Constant Alpha 0 2 gt Grid Search You can click Grid Search button to identifying the optimum smoothing parameters Results Storage sptions GK f Cancel FIGURE 72 Exponential Smoothing Form 4 Zaitun Time Series also provides Grid Search facility to facilitate user in searching smoothing constant values in yielding the least MSE value You can search smoothing constant value by determining minimum and maximum boundary and increment interval Application will search the combination of smoothing constant value in interval above which has the least MSE N combination default 10 will be shown To choose the best value of smoothing constant click the value in list and click Select This button HE Double ES Holt Grid Search Search Patameter Start parameter at gamma oo Best Resuli asni Gor oe a aa ea e E Tacrement by alpha oo 86 0 100 O10 S Stop parameter at 10 Solution i oo g 2 34093 236168 2 35665 2 38992 2 42646 246976 249592 2 59489 279435 275245 1 35057 116046 1 99352 1 39761 159549 1 33320 1 15730 0
48. ndows Help ie lt 3 i Trend Analysis hel Decomposition a2 Moving Average f Exponential Smoothing M E Neuralietwork Tipe Description competitor Series competitor Outlet Series Dutlet PopulationGrowth Series PopulationGrowth Promotion Series Promotion Sales Series Sales FIGURE 87 Linear Regression Menu 2 Determine the dependent variable and the independent variables on the dialog Choose a Sales variable as dependent variable and Promotion Competitor Outlet and PopulationGrowth and then click OK te Linear Regression Analysis List of Vanables Dependent Beles Eek Somme Promotion competitor Cancel Outlet PapulatonGbrowth FIGURE 88 Linear Regression Analysis Dialog Click Results button to show the Select Result View Dialog and set the result of analysis Check the check box of the options appear if you want Zaitun Time Series to shows that result ES Linear Regression Select Result View Table Model Sianimary Residuals Durbin Watson E ANDWA Z Renression Coefficients Confidence intervals E vir E Partial correlation H Actual predicted and residual Foreattes step 1 Gava Graphic Residual graph V Residual vs predicted graph EA Namal probability plot for residual prey i a FIGURE 89 Select Result View Dialog If Forcasted option in checked yo have to set the test values by clicking the Set
49. or 55E Mean Squared Error MSE Mean Percentage Error MPE Mean Absolute Percentage Error MAPE 21 746563 Projest View Variable View Result View Status FIGURE 66 Table of Moving Average Model Summary Zaitun Time Series Beta Edition paper C Program Files Aleebra Zaitun Time Series Sample Data paper zft AG E ie a 3 Moving Average paper Moving Average Model Summary Single Moving Average Table Project View Variable View Result View Status FIGURE 67 Table of Forecasted Value 2 Graphics a Actual and Predicted Shows a line plot for actual and predicted values of moving average model b Actual and Smoothed Shows a line plot for actual and smoothed values of moving average model c Actual and Forecasted Shows a line plot for actual and forecasted values of moving average model d Actual vs Predicted Shows a scatter plot between actual and predicted values e Residual Shows a line plot for residual values of moving average model f Residual vs Actual Shows a scatter plot between residual and actual values g Residual vs Predicted Shows a scatter plot between residual and predicted values aai Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Actual and Smoothed Graph Project View Variable View Result View Status FIGURE
50. orecasting United Stated of America Prentice Hall Inc Kutner Michael H et al 2005 Applied Linear Statistical Models McGraw Hill Irwin Montgomery Douglas C 1990 Forecasting and Time Series Analysis McGraw Hill Inc Prechelt Lutz 1998 Automatic Early Stopping Using Cross Validation Quantifying the Criteria Fakultat fur Informatik Universitat Karlshure Karlshure Germany Sarle S Waren 2002 Neural Network FAQ Zhang Guoqiang B Eddy Patuwo and Michael Y Hu 1998 Forecasting with Artificial Neural Networks The State of The Art International Journal of Forecasting Graduate School of Management Kent State University Ohio USA
51. oup Sime Select variable or group Type Descnphon Foreign Change Group Group of USDollarChange Ven Change Indonesian Change Sees Indonesia Exchange Rate fomdanuarn 1980 to Dec US Dollar Change Sees USDollarsChange TensChange Series feresChange OK Cancel FIGURE 26 Select Variable Dialog The default view is the spreadsheet view To change the current view of a variable click on the Variable View Combo Box on the top of the Variable View pane You can switch to graphic view or statistics view YenxChange February 2004 April 2004 June 2004 August 2004 FIGURE 27 Spreadsheet View Spreadsheet View shows variable values on a grid it makes it easy for you to input or edit variable values by pressing numeric keys directly from keyboard You can also paste values from an external program like Excel by right clicking the grid and selecting Paste menu Zaitun Time Series newproject SS February 2004 March z004 April 2004 May 2004 Select Al CtritA dune 2004 July 2004 FIGURE 28 Pasting Data into Spreadsheet View Graphic View shows variable values on a line chart It makes it easy for you to analyze graphically the components of time series data of a variable You will soon know whether the variable contains trend cyclic seasonal and irregular component Zaitun Time Series sunspot C Program Files Waitun Time Serjes Waitun Time
52. phics The details of them are described here 1 Tables a Model Summary Shows the summary of the neural network model b Actual Predicted and Residual Shows actual predicted and residual values of the neural network model c Forecasted Shows forecasted values from neural network model as many steps of data you want to forecast Zaitun Time Series Beta Edition sunspot C Program Files Algebra Zaitun Time Series Sample Data sunspot zft A E x M Neural Network sunspot Neural Network sunspot Neural Network Model Summary Actual Predicted and Residual Forecasted Actual and Predicted Graph Actualand Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph ANN Model Summary for sunspot b Variable Included Observation 1247 After Adjusting Endpoints Network Archiecture Input Layer Neurons Hidden Layer Neurons Output Layer Neurons Activation Function Back Propagation Learning Learning Rate Momentum Criteria Project View Variable View Result View Status FIGURE 112 Neural Network Model Summary Zaitun Time Series Beta Edition sunspot C Program Files Algebra Zaitun Time Series Sample Data sunspot zft Neural Network sunspot Neural Network sunspot Neural Network Model Summary
53. ransform Variable SEE Transformed arable Trarefornation Type passenger G Differencing O Seasonal differencing lag a Cancel Natural logarithrn Loganthm base io 3 Square root New variable name FIGURE 33 Transform Variable Dialog 2 Select a variable you want to transform and select the transformation type 3 Determine the new variable s name and then click the OK button Zaitun Time Series will create a transformed variable and add it into the current project Zaitun Time Series passenger C Program Files Vaitun Time Series aitun lime Se File view Analysis Tools Windows Help ah Description dpassenger Series Differencing transformation from passenger passenger Series FIGURE 34 Project View after Transforming a Variable Exporting The Data Zaitun Time Series provides a facility to export the data created by Zaitun Time Series to another format There are 2 formats available CSV file and Excel File Zaitun Time Series will export all of variables in the current project into a new CSV or Excel File but it will not export the group data and the result data To export the current Zaitun Time Series project into a CSV file 1 Click File gt Export gt Export to CSV Zaitun Time Series passenger C Program Files Vaitun lime Series Vaitun Ti New ChreN Open ctrl o Ets
54. rediction of the next movement of the stock market data The result of prediction helps them to decide whether to buy or sell the market or do nothing To import a live stock market data in the current Zaitun Time Series project 1 Click the Import Stock button on the top of Project View to open Import Stock Dialog Import Stock Stock Informaticn Server Yahoo Finance Symbol Frequency Monthly Tamed Range 2009 AA 2009 12 Preview Stock Desenptian Name Descnption FIGURE 49 Import Stock Dialog 2 Determine the server and symbol on stock information You can view the list of symbol by clicking the List button On the Stock List Dialog you can add edit and delete the symbol Stock List Symbol Description m l Add Edt Deite FIGURE 50 Stock List Dialog 3 Click the Download Data from Server button to preview imported data import Stock al ie ad E Steck Infomation Server YahooFinance s a Symbol HE a s S mem fron Sever Frequency Monthly Time Aange 20097 s 200912 Preview Yolurne Adj Close 2009 06 01 14 29 1425 14 25 14 29 000 14 29 2009 05 01 14 29 14 29 14 29 14 29 000 14 29 2009 04 01 14 29 14 29 14 29 14 29 gg 14 29 2003 03 02 14 29 74 249 7429 74249 oon 74249 2009 02 02 13 00 1433 T300 14 29 1800 14 29 2009 01 02 15 71 16 29 1258 1359 3700 13 53 stock a e AAAA Description FIGURE 51 Pre
55. rjes Waitun Time Series Sample Data sunspot zft w L Neural Network sunspot gt Neural Network sunspot x Neural Network Model Summary Actual Predicted and Residual Forecasted Actual and Predicted Graph ActualandForecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph 3 2 m Q w 150 Predicted Project View Variable View Result View Status FIGURE 115 Residual vs Predicted Graph References Abraham Bovas et al 1983 Statistical Methods for Forecasting Canada John Wiley amp Sons Crone Sven F 2004 Stepwise Selection of Artificial Neural Networks Models for Time Series Prediction Department of Management Science Lancaster University Management School Lancaster UK Du K L and M N S Swamy 2006 Neural Network in Softcomputing Framework London Springer Drossu Radu Zoran Obradovic 1995 Efficient Design of Neural Network for Time Series Prediction School of Electrical Engineering and Computer Science Washington State University Washington USA Enders Walters 2004 Applied Econometric Time Series New York John Wiley Sons Inc Gujarati Damodar N 2003 Basic Econometric fourth edition New York McGraw Hill Hamilton James D 1994 Time Series Analysis New Jersey Princeton University Press Hanke John E and Reitsch Arthur G 1986 Business F
56. s and to show the result views 8 The selected result views on previous step will be viewed as several tabs on Result View panel Exponential Smoothing Analysis Result The result views of exponential smoothing analysis in Zaitun Time Series are grouped into two categories tables and graphics The details of them are described here 1 Tables a Model Summary Shows the summary of exponential smoothing model b Exponential Smoothing Table Shows actual smoothed trend seasonal predicted and residual values of exponential smoothing model c Forecasted Shows forecasted values from exponential smoothing model as many steps of data you want to forecast Zaitun Time Series Beta Edition maxtemp C Program Files Algebra Zaitun Time Series Sample Data maxtemp zft BAR Wiincnaie Helin B V X Windows Heip EX Pa esa ty Sate lt NIV Double ES Holt maxtemp Exponential Smoothing Model Summary Double Exponential Smoothing Holt Table Actual and Predicted Graph Actual and Smoothed Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Actual _Smoothed rend _ Predicted Residual d 27 1872 5 6524 19 8719 25 7000 26 4340 0 5679 33 0396 in ia 21 9000 22 4102 3 1054 27 0019 16 4000 16 6905 5 1969 19 3047 14 1000 13 8394 3 3203 11 4936 14 5000 14 2690
57. s or often called Neural Networks is a computation technique which has made significant progress in recent times Neural networks have proven their capability of handling various problems in a number of scientific disciplines Neural networks have a powerful ability called universal approximation they can approximate all multivariate continue functions to every level of accuracy including for non linear functions The ability of neural networks in universal approximation has been used by some researchers to forecast time series data in various kinds of data The researches show that Neural Networks have a satisfactory performance in forecasting time series data Neural networks mechanisms imitate biological neural network mechanisms Like biological neural networks neural networks consists of neurons which are connected to each other and operate in parallel The information processing mechanism in every neuron is adopted from the biological neuron Neurons in a neural network are grouped into several layers Every layer can have one or more neurons There are three layers in neural network architecture they are the input layer the output layer and the hidden layer The function of the input layer is for data entry data processing takes place in the hidden middle layer and the output layer functions as the data output result The following illustration shows the architecture of neural networks INPUT 1 INPUT 2 INPUT 3 INPUT 4
58. step will be viewed as several panels on Result View tab page Trend Analysis Result The result views of trend analysis in Zaitun Time Series are grouped into two categories tables and graphics See the details below 1 Tables a Model Summary Shows the summary of trend model b Actual Predicted and Residual Show actual predicted and residual values of trend model c Forecasted Shows forecasted values from trend model as many steps of data you want to forecast Zaitun Time Series Beta Edition passenger D data skripsi passenger zft Eelk ol File Wew Analysis Tools Windows Help amp xX 51 Ee led SF Trend Analysis passenger fend Analyse Medel Sunma Actual Predicted and Residual Forecasted Actual andPredcted Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual vs Actual Graph Residual vs Predicted Graph Trend Analysis Model Summary for passenger Model Summary gt Variable Included Observation Linear Trend Equation Yt 90 560 2 597t R 0 919856 R Squared 10 846136 R Sguare Adjusted 0 999675 Sum Square Error SSE 224439 343053 Mean Squared Error MSE 1753 432368 Project View Variable View Resuit View Status FIGURE 58 Table of Trend Analysis Model Summary Zaitun Time Series Beta Edition passenger D data skripsi passenger zft EER all file View Analysis Tools
59. tall Zaitun gie Setup will install Zaitun Time Series in the following directory To install to this directory click Next To install into a different directory click Browse and select another directory You can choose not to install Zaitun Time Series by clicking Cancel to exit Setup oe E Destination Folder CiProgramFilestzaltun Time Seriesi Browse Installer20 Freeware EEE FIGURE 3 Choose Destination Location Screen 5 Ready to Install Screen appears Click Install to begin the installation iz Zaitun Time Series Setup Ready to Install aa gt ig _ l Click Install to begin the installation IF you want to review or change any of your installation settings click Back Click Cancel to exit the wizard folate l n Freeware ig Zaitun Time Series Setup Installing Zaitun Time Series Please walt while the Setup Wizard installs Zaitun Time Series This may take several minutes Status Copying new Files COOLE FIGURE 5 Installing Zaitun Time Series Screen 6 After the installation is complete setup will inform you that the installation is successful You may then launch Zaitun Time Series by clicking on Launch Zaitun Time Series check box Click Next to continue and finish the setup iv Zaitun Time Series Setup Completing the Zaitun Time Series Setup Wizard Click the Nest button to exit the Setup Wizard Y 2 Ar
60. te Variable Dialog 3 Enter the new variable group s name and then click the OK button Zaitun Time Series will create a new variable group that has same value as the source variable group Zaitun Time Series newproject Unsaved Sey Geese Tags Winds tee Name Type Dascipton Foreignsehange Group Group of USGollarschange Yensichange Indonesianchange Series Indonesia Exchange Rate From January 2004 to Decemb Hapanschange Yenkchange lt ei i Usp llarschHange Series USDollarxchange Yenschange Series Yens Change FIGURE 20 Data View Screen after Duplicating the Variable Deleting A Variable Group You can also delete a variable group you have created To delete a variable group 1 Select the variable group you want to delete Zaitun Time Series newproject Unsaved Tools Windows Sammons Satis eoo pi a MO ae eae a SSS Name Tepe Description Foreign Change Group Group of USDollar Cchange Yenktchange Indonesian Cchange Series Indonesia Exchange Rate from January 2004 to Decemb Japanechange Japans Change UsCollar chande USQollarkchange Yens Change Series Yenschange FIGURE 21 Selected Variable 2 Click the Delete button A confirmation dialog appears Click Yes if you are sure you wish to delete the selected variable group Delete Variable 2 Are you sure you want to remove variable YenXChange FIGURE 22 Confirmation Dialog 3 If
61. tion of the relation So we can use the adjusted R pR n A DSSE n p SST R where 0 lt R lt 1 Diagnosing of the Model Assumption 1 Linearity This assumption can be diagnosed by ploting the residual e and the predicted ee If plot look like random pattern near of e 0 so this assumption is accepted 2 Normality Normality can be checked by Normal Probability Plot NPP If plot look like straight line so this assumption is accepted 3 Homoscedasticity This assumption can be diagnosed by ploting the residual e and the predicted Y If plot look like random pattern near of e 0 so this assumption is accepted 4 Autocorrelation This assumption can be diagnosed by ploting the residual at time t e and the time t If plot look like random pattern so this assumption is rejected 5 Multicollinearity This assumption can be checked using Variance Inflation Factor VIF If the highest value of VIF gt 10 so this assumption is accepted Linear Regression Analysis with Zaitun Time Series For example we can try to analyze multiple linear regression of an annual total product sales as the dependent variable and promotion and competitor outlet and population growth as independent variables To analyze linear regression of that time series data with Zaitun Time Series 1 Click Analysis gt Linear Regression Zaitun Time Series Sales C Documents and Settin Mew Analysis Tools wi
62. types among those components they are multiplicative and additive Multiplicative type assumes if data value grows up then seasonal pattern will grow up too While additive type assumes that data value resides in a constant wide at the middle of trend In the decomposition method every cycle of data is assumed to be part of a trend The decomposition method equations Multiplicative type Additive type The Seasonal Index value is calculated by using a ratio to moving average method Decomposition Analysis with Zaitun Time Series Zaitun Time Series performs decomposition analysis on time series data To perform decomposition analysis on a time series variable 1 Click Analysis gt Decomposition Zaitun Time Series passenger C Program Files Waitun Time SeriesVaitun Tir Moving Average Exponential Smeathing Linear Regression s Correloaranr Neuralletwork Name pe DS iption n dpassenger Series Differencing transformation from passenger passenger Series FIGURE 79 Decomposition Menu 2 Select Variable Dialog appears Choose a variable you want to 3 analyze with decomposition analysis and then click OK ER Select Analyzed Variable Analyzed Vanable a Caneel FIGURE 80 Select Analyzed Variable Dialog The Decomposition form will appear Determine the seasonal length decomposition method multiplicative or additive and the used trend model There are severa
63. view Imported Data Determine imported stock s name and the description on stock description Click the OK button Zaitun Time Series will add this imported stock into the current project The imported stock data contains a stock data type and 5 variables data type which consist of open close high low and volume values of the stock data Zaitun Time Series Jator ichange at fee eee eee Name Type Description HEG Stock HEG HEG close Series HE close HE high Series HEG_ high HG low Series HE low HENS open Series HES open HEG_volurrie Series HEG volume FIGURE 52 Imported Stock Trend Analysis Chapter Trend Analysis Overview Linear Trend Linear trend is a simple function described as a straight line along several points of time series value in time series graph Linear trend has a common pattern Te a b Y Where Ti Trend value of period t Constant of trend value at base period Coefficient of trend line direction Yt an independent variable represents time variable usually assumed to have integer value 1 2 3 asin the sequence of time series data There are several methods that can be used to find the linear trend equation of a time series Most commonly used is least squares method This method finds the coefficient values of the trend equation a and b by minimizing mean of squared error MSE The formula is dT RY UT n gt Y Y Y a Y bT t Nonlinear Tren
64. vs Actual Shows the scatter plot between residual and actual values f Residual vs Predicted Shows the scatter plot between residual and predicted values Zaitun Time Series passenger C Program Files Waitun Time Series aitun Time Series Sample Data passenger zft e X 8 Ble Yew analysis Toos windows Hep 3x las F 3 Trend Analysis passenger gt xX Trend Analysis Model Summary Actual Predicted and Residual Actual and Predicted Graph 73 82 91 100 109 116 127 Project Yiew Variable View Result View Status FIGURE 6O Actual and Predicted Graph Moving Average Analysis Moving Average Overview There are several methods which can be used to smooth time series data by moving averages They are the Single Moving Average and the Double Moving Average methods Both of them use several past data points to forecast the future Single Moving Average The Single Moving Average method uses the last t periods to create a forecast The new average value is calculated by removing the oldest value and replacing it with the newest value This method is suitable for stationary data and for data which does not contain trend or seasonal components Let us have N points of data and use T observations to calculate the average value notated as MA T It is described as nee T Yt Loe Yn Initialization group Testing group Time Moving Average Fore
65. y Plot NPP Zaitun Time Series Sales C Documents and Settings anas Wy Documents Sales zft Regression Analysis Model 1 2 2222 Linear Regression Model Summary ANOVA Coefficients Actual Predicted and Residual Forcasted Residual Graph Residual vs Predicted Graph Normal Probability Plot Normal Probability Plot a Residual Vs Expected Residual Residual 0 Expected Residual Project view Variable View Result View Status FIGURE99 Normal Probability Plot Correlogram Chapter Correlogram Overview Correlogram or Autocorrelation Function ACF is a graphic of autocorrelation values from several time intervals in time series data ACF explains how big the successive data correlation in a time series data ACF can be used to determine whether a time series data is Stationary or not ACF represents comparison between covariant on lag k and its variant ACF formulated as follows 5 Y Y Y Pi tec t Sir 1 Where P ACF coefficient in ag k T The number of observations the amount of observed period Y Observation in t period y Mean aa Observation in t k period ACF k has value started from 1 to 1 If ACF value on every lag is O hence the data is stationary As a rough rule lag length needed to analyze is one third or a quarter of the number of observations of a time series data Also to determine whether a tim
66. zed values of decomposition model opan CER Help Ere K Zaitun Time Series passenger C Program FilesWaitun Time Seriesaitun Time Series Sample Data passenger zft L Trend Analysis passenger Decomposition passenger SK Decomposition Model Summary Decomposition Table Forecasted Actual Predicted and Trend Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Detrend Graph Deseasonal Graph Detrend Graph 127 Project View Variable View Result View FIGURE 85 Detrended Graph FEN 4l x ___Trend Analysis passenger Decomposition passenger l z i Decomposition Model Summary Decomposition Table Forecasted Actual Predicted and Trend Graph Actual and Forecasted Graph Actual vs Predicted Graph Residual Graph Residual vs Actual Graph Residual vs Predicted Graph Detrend Graph FDeseasonal Graph Deseasonal Graph 100 109 118 127 Project View Variable View Result view Status FIGURE 86 Deseasonal Graph Linear Regression Chapter Analysis Linear Regression Analysis Overview Linear Regression estimates the coefficients of the linear equation involving one or more independent variables that best predict the value of the dependent variable For example we can try to predict a product total yearly sa

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