Grocer 1.0, an Econometric Toolbox for Scilab: a Scilab Point of View
Contents
1. ans 4 gt myts dates ans Figure 1 synoptic of the function ols Input of ols strings vectors matrices timeseries y explolist v Initial inputs except noprint J exploy Tg explouniv ee matrices X Y names of variables boolean for the presence of ts in the regression v explox y ols2 a results tlist containing the data the estimated parameters and the associated statistics drawx printmat lt gt prtuniv pltuniv gt pltseries0 l ji drawy prints results on screen graphs residuals fitted values together with true values a results tlist containing the data the estimated p rameters the associated statistics the names of the Wariables the time period if any 1 amp gt gt 1 ha r NE prtuniv pltuniv statfore 5 ae prtchi for example prints statistics and p values l arim 4 armo of specification tests prifish W Y set of specification tests a results tlist containing the ols results tlist the values of the statistics and their p values Legend function name of a Grocer function output output from ols function set of Grocer functions input input of ols function intermediate results interm2. or n 7 ccg_mi lagts ccg_m3 0 1103030 4 1064521 0 0000876 cte 0 4862431 5 23963 0 0000010 ppy_m1 0 0497842 6 3302334 9 083D 09 x tests results 19 Aak kkk K test test value p value Chow pred fail 50 0 9958242 0 5069009 Chow pred fail 90 0 8716775 0 5538006 Doornik amp Hansen 0 8382420 0 6576246 AR 1 4 1 233487 0 3026397 hetero x_squared 0 5730995 0 7507011 x The model selected by the algorithm is here the only one that has been displayed along with the statistics of the associated specification tests The display shows however that this model has been selected among several models whose properties are almost equivalent ending reason stage 2 models selected by bic criterion It can be worthwhile to print these models Since the results have been saved in tlist rman this can be done by running gt prtauto_multi rman stage 2 models which shows all the models here there only 2 selected at the end of stage 2 stage 2 models model 1 ols estimation results for dependent variable gyman estimation period 1979q2 2002q4 number of observations 95 number of variables 4 R72 0 4970310 ajusted R 2 0 4804496 Overall F test F 3 91 29 975222 p value 1 439D 13 standard error of the regression 0 8614509 sum of squared residuals 67 530894 DW 0 2 2836444 Belsley Kuh Welsch Condition index 13 variable coeff t statistic p value lagts ccg_m3 lagts ccg_m2 0 0845522 2 934
3. reader may wonder why bother remaking what already exists in Scilab The obvious answer is that ols is not leastsq To explain why let us start from what ordinary least squares are for an econometrician 2 1 Ordinary least squares from an econometrician point of view For an econometrician as for anyone else ordinary least squares perform the following min imisation T i E E min Y Xb min Y Xb Y Xb ee ye bitit Rte min leer ara lyen which leads to the well known result b X X X y This formula is exactly leastsq s output However from the perspective of an econometrician ordinary least squares also entails the calculation of many associated statistics such as T K i the variance of the estimated parameters 6 yH X 07 Y Xb Y Xb with t 1 a Y Xb the vector of estimated residuals e the variance of the estimated parameters V b 62 X X 7 e the Student statistics associated with each coefficient f 2 Gi e the p value associated with the hypothesis that a coefficient is nil p P ISr x gt Ts bi 0 where S p_ designs the Student law with T k degrees of freedom e the R square R 1 ST Gop with y mean of y and SCR Say ti e the adjusted R square R 1 SL o T 1 T 1p 4 2 e the Durbin and Watson statistics DW a ae t t ols computes all these statistics However an applied econometrician s work does not stop with
4. time period if the user has provided the string cte or const then the corresponding vector is created at the end of the program its size being determined by the size of the other variables in the regression collect the names of the variables in a vector of names the corresponding values in a matrix Y for exploy and X for explox define a boolean indicating the presence or absence of time series in the regression if there is a time series in the regression then the bounds of the regression will be displayed at the end The tlist of results The arguments of the tlist of results called say rols are the following rols meth ols this is the econometric method this argument allows a wrapper function prtres to recognise what display function to use rols y y data vector rols x X data matrix rols nobs observations rols nvar variables rols beta b rols yhat y rols resid residuals rols vcovar estimated variance covariance matrix of beta rols sige estimated variance of the residuals rols sigu sum of squared residuals rols ser standard error of the regression rols tstat t stats rols pvalue pvalue of the betas rols dw Durbin Watson Statistic rols condindex multicolinearity cond index rols prescte boolean indicating the presence or absence of a constan
5. 1329 0 0042328 ccg_mi lagts ccg_m3 0 1103030 4 1064521 0 0000876 cte 0 4862431 5 23963 0 0000010 ppy_m1i 0 0497842 6 3302334 9 083D 09 20 aic 0 2570812 bic 0 1495495 hq 0 2136303 model 2 ols estimation results for dependent variable gyman estimation period 1979q2 2002q4 number of observations 95 number of variables 5 R72 0 5048903 ajusted R 2 0 4828855 Overall F test F 4 90 22 944477 p value 4 332D 13 standard error of the regression 0 8594292 sum of squared residuals 66 475665 DW O 2 2192735 Belsley Kuh Welsch Condition index 13 variable coeff t statistic p value lagts sto_m2 lagts sto_m1 0 0757736 2 1789326 0 0319490 ypa_mi lagts ypa_m3 0 0524032 2 2846024 0 0246872 ccg_mi lagts ccg_m3 0 0998390 3 6582228 0 0004275 cte 0 4926179 5 3029259 8 081D 07 ppy_m1 0 0503658 6 4470266 5 544D 09 aic 0 2517778 bic 0 1173632 hq 0 1974642 As shown in this example as in many other instances when it has been used at the French Ministry of Finance the function automatic has proved a very useful tool for a quick and 21 robust estimation of econometric relationships when a great number of exogenous variables is potentially relevant Conclusion Grocer is a package that performs most standard econometric methods and some less stan dard but very useful ones Grocer is due to evolve regularly and some new features are already underway A few procedures existing in some commercial packa
6. Grocer 1 0 an Econometric Toolbox for Scilab a Scilab Point of View Eric Dubois Direction de la Pr vision et de Analyse Economique T l doc 679 139 rue de Bercy 75012 PARIS e mail Grocer toolbox free fr Abstract In his review of Scilab for the Journal of Applied Econometrics Mrkaic 2001 concludes a dedicated econometric package would significantly increase the appeal of Scilab to applied econometricians Grocer 1 0 available at http dubois ensae net grocer html aims at filling this gap and even more Grocer programming strategy is exposed through the example of ordinary least squares and the paper shows how the econometrician needs imply a very different strategy from the one behind Scilab function already performing ordinary least squares and much more programming This paper also presents Grocer main originality with respect to other econometric software which consists in a package performing automatic estimation Scilab is a matrix oriented software very similar to Matlab and Gauss software that are much used by econometricians So Scilab should prove very useful to them In his review of Scilab for the Journal of Applied Econometrics Mrkaic 2001 shared this opinion but concluded a dedicated econometric package would significantly increase the appeal of Scilab to applied econometricians Grocer 1 0 available at http dubois ensae net grocer html aims at filling this gap and
7. ading function so the overloading function begins by determining the overlapping time period of the two time series and then performs the operation on the 2 vectors of values restricted to this overlapping period Time series sometimes have NA Non Available values For instance French macroeconomic data over the last century do not exist during the 2 world wars such a series will be NA for the years 1914 1919 and 1930 1945 So Grocer ts comply with NA values nan in Scilab code This possibility comes along with some useful flexibility with respect to estimation the user can choose a discontinuous estimation period such as 1920 1939 1946 2004 in order to estimate over periods with non NA values and if the user does not specify it Grocer functions are able to estimate a time period compatible with the data more on this below A few specific functions have been programmed to lag function lagts differentiate func tion delts time series compute their growth rate growthr aggregate monthly time series to quarterly m2q or quarterly to annual m2a extrapolate a time series by the value overlay or the growth rate extrap of another one Lastly time series can also be created by loading external data through an interface with Excel 2 4 The flexibility of econometric functions with respect to inputs and their implications for the programmer All high level econometric functions allow the user to enter various types of data
8. ands gt load SCI macros grocer db bdhenderic dat load the database that is given with Grocer package gt bounds 1964q3 1989q2 set the same time bounds as Hendry and Ericsson gt rhe ols delts 1m1 lp delts 1p delts lagts 1 1m1 lp ly gt ynet lagts 1 1m1 lp ly cte variables have been entered between quotes their names are saved for the display variables 1m1 1p ly rnet are time series the estimation involves the specific functions delts and lagts as well as the overloaded function ts_m_ts And here is the result of the corresponding Grocer session 11 ols estimation results for dependent variable delts 1m1 lp estimation period 1964q3 1989q2 number of observations 100 number of variables 5 R72 0 7616185 ajusted R 2 0 7515814 Overall F test F 4 95 75 880204 p value 0 standard error of the regression 0 0131293 sum of squared residuals 0 0163761 DW O 2 1774376 Belsley Kuh Welsch Condition index 114 variable coeff t statistic p value delts 1p 0 6870384 5 4783422 3 509D 07 delts lagts 1 1lm1 lp ly 0 1746071 3 0101342 0 0033444 rnet 0 6296264 10 46405 0 lagts 1 1m1i lp ly 0 0928556 10 873398 0 cte 0 0234367 5 818553 7 987D 08 x When properly rounded the coefficients are the same as those provided by Hendry and Ericsson Student s T are displayed while Hendry and Ericsson presented figures bet
9. d printmat e similarly some results are graphed at the end of an estimation these graphs are also obtained by a specialised function called pltuniv again if the results tlist is present in the environment then these results can be graphed again without resorting to a re estimation of the model Scilab graphic functions are used but they had to be adapted to time series this is the purpose of function pltseriesO which also extends Scilab graphic functions in some directions for instance it allows to graph simultaneously series with curves and bars e the results thst can also be used as an input of many specification tests again the cor responding functions are generally built upon a low level function and use specialised printing functions prtchi and prtfish Besides ols there are numerous functions applying econometric methods to a single equation model instrumental variables least absolute deviations regression non linear least squares logit probit tobit Cochrane Orcutt ols and maximum likelihood ols regression for AR1 errors ols with t distributed errors Hoerl Kennard Ridge Regression Huber Ramsay Andrew or Tukey robust regression using iteratively reweighted least squares Theil Goldberger mixed estimation Beyond their technical specificities the corresponding functions use basically the same bricks as ols All functions can be applied to time series as well as vectors matrices and strings They therefore
10. e with ols the function automatic has been tested on an example already published namely one presented in Hendry and Krolzig 2000 Another example taken from Dubois and Michaux 2004 is presented here contrary to the estimation taken from Hendry and Krolzig the work done for this article has been realised directly with Grocer The objective of the paper was to build relationships between business surveys and the manu facturing production Since business surveys are available more rapidly that the manufacturing production the use of such relationships is in fact an important tool in the macroeconomic exercises that are regularly performed at the French Ministry of Finance for instance for the preparation of the State Budget Since firms do not assess directly their manufacturing production during a definite period of time but answer qualitative questions such as do you think that your production has increased decreased or stagnated during the last three months many variables are potentially relevant to forecast the manufacturing production This made the use of the automatic function especially attractive Seven models were estimated according to the month in the quarter when the survey was performed and the quarterly horizon considered For example the model estimated for the manufacturing production of the current quarter when the survey of the first month of the quarter has been released was built by applying automatic to the foll
11. ediate results in function ols other results results derived from ols results 17 18 19 20 21 gt myts series ans PP We ND oa nN Aere A more explicit representation of the dates can be recovered through Grocer function num2date gt num2date myts dates myts freq ans l4q1 l4q2 4q3 l4q4 I5q1 And the display of a time series does not provide the internal structure of the tlist but a more user friendly representation with the dates and the series facing one another gt myts myts 4qi 2 1 4q2 1 4 4q3 3 2 4q4 4 5 5qi 1 5 This representation makes use of the power of tlists in Scilab this user friendly display is provided by function ts_p that overloads the normal display of a ts But the main interest of using a tlist representation is to be able to define standard opera tions or functions on tlists addition multiplication division logarithm The corresponding functions ts_a_ts ts_m_ts 7 ts_r_ts 7 ts_log all in all 27 overloading functions have consequently been written As regards an operation involving two time series such as the addition or the multiplication there is a big difference with the same operation on 2 vectors the time series can be of different size because they do not cover exactly the same time pe riod provided they have the same frequency this condition is first tested by the overlo
12. even more Grocer contains most standard econometric procedures Numerous methods applying to single equations are available from ordinary least squares to limited dependent methods through non linear least squares instrumental variables estimation Contrary to the Scilab function performing ordinary least squares which is rather rough each Grocer estimation comes with a bunch of statistics standard in econometric applications such as the Standard Error of the Regression the R squared Student s statistics the Durbin and Watson statistic Moreover presented at the first Scilab International conference at INRIA Rocquencourt FRANCE 2004 the 2 amp 3 of november 1 Available at http scilabsoft inria fr numerous specification tests can be applied to the results of these regressions such as normality tests ARCH tests Ramsey RESET test autocorrelation tests The treatment of non stationary variables which has now become inescapable when working with timeseries can be performed with Grocer The standard Dickey Fuller Phillips and Perron KPSS unit root tests are in particular available along with the Engle Granger and Johansen coin tegration methods Up to date filters Hodrick Prescott Baxter King or Christiano Fitzgerald have also been implemented The treatment of multiple equations models can be done with Grocer Standard old fashioned simultaneous equations methods Zellner Seemingly Unrelated Regressions t
13. ges and some more rare but nevertheless useful methods notably in the bayesian field remain to be implemented The matrix oriented nature of Scilab will make it easy to stay at the forefront of the econometric science And the great similarity between Scilab and Matlab or Gauss will help as well Acknowledgements I wish to thank the Scilab team for their precious advices James Le Sage for having provided the basis of so many grocer functions Emmanuel Michaux for his faithful use and testing of Grocer Catherine Dubois Benoit Bellone and Alexandre Espinoza for their careful reading and useful comments on this article 22 References Dubois 2004 Grocer 1 0 An Econometric Toolbox For Scilab user manual available at http dubois ensae net grocer html Dubois and E Michaux 2004 Etalonnages a l aide d enqu tes de conjoncture de nouveaux r sultats forthcoming in Economie et Pr vision available at http dubois ensae net papers html D F Hendry et N R Ericsson 1991 Modelling the demand for narrow money in the United Kingdom and the United States European Economic Review pp 833 886 D F Hendry and H M Krozlig 1999 Improving on data mining reconsidered by K D Hoover and S J Perez Econometrics Journal n 2 pp 41 58 D F Hendry and H M Krozlig 2000 Computer Automation of General to Specific Model Selec tion Procedures Journal of Economic Dynamics and C
14. matrices vectors time series as well as strings Two kinds of strings are allowed first the strings const or cte that avoids the user to create the constant vector or time series relevant for her problem second the name of an existing variable between quotes The variable myts presented above can for instance be entered as such e g ols myts cte for the regression of myts on a constant or between quotes ols myts cte In the last case Grocer function is able to display the names of its inputs These two characteristics flexibility and the possibility to keep trace of the names of the variables has two major consequences the constraint it imposes to the programmer and the user as regards the names of the variables the need to transform the input variables into matrices to perform the calculations behind each econometric procedure The first consequence results from the fact that when a variable is entered as a string the true variable must be recovered by Scilab command evstr to recover the ts myts entered The string cte that is an abbreviation of the French world constante was first implemented to maintain compatibility with earlier versions of Grocer used by some forerunners both abbreviations are available in the 1 0 version 3Some other usual variables such as trends could also be treated this way this is left for further releases as myts you have to run evstr my
15. ontrol 25 6 7 pp 831 866 K D Hoover and S J Perez 1999 Data mining reconsidered a general to specific approach to specification search Econometrics Journal n 2 pp 167 191 M Mrkaic 2001 Scilab as an Econometric Programming System Journal of Applied Econometrics vol 16 n 4 July August pp 553 559 23
16. or conditional expressions Scilab relative slowness as regards these types of operations is certainly a more important drawback than for the other Grocer programs but the execution time on a modern computer remains lower than a minute for the most usual applications and even if there are loops in this program most calculations still involves matrices and so once again Scilab philosophy remains rather well adapted to the problem e the function uses many bricks used by other single equations methods explox and exploy to transform the input variables into matrices 5 low level specification tests for default use and potentially all specification tests for a sophisticated user printing functions e a function the one that performs the specification tests is itself created in function automatic this is made possible by the existence of Scilab instruction deff e the results take the form of a voluminous results tlist that includes itself other results tlists to display the results of stage 0 stage 1 and if any stage 2 estimations it is convenient to store them as standard estimation results that take ordinarily the form of tlists Scilab flexibility with respect to tlists allows easily such tlist imbrications Informations about pc gets are available at http www doornik com pcgive pcgets index html 15 3 2 An example Dubois and Michaux 2004 forecasting models of manu facturing production from a business survey As don
17. owing set of variables e the endogenous variable was the growth rate of the manufacturing production variable called gyman in the database the exogenous ones were e lags 1 to 3 of the endogenous variable lagts gyman lagts 2 gyman lagts 3 gyman 4 variables e values in each first month survey of the opinion about past production ypa the opinion about future production ppy opinion about global orders ccg opinion on the invento ries level 4 variables e lags 0 to 4 of the first difference of each of these 3 variables 16 variables e aconstant 1 variable The total number of variables was therefore 24 Default options were used except for the printings that are here reduced for the sake of brevity This entailed the following Grocer command gt load SCI scied fourgeaud data2 dat gt bounds 1979q2 2002q4 16 Figure 3 synoptic of the function automatic Input of automatic strings vectors matrices timeseries vector y i its name separation of the exogenous variables and the options function called test_func performing specification tests names used for their display matrix X its name bounds if any def_results a results tlist filled with the first argument type of the tlist and names of the following arguments and other invariable elements initial model yes test if this is the final model ne auto_
18. puter based general to specific method to recover with great reliability the underlying data generating process 3 1 An outline of the automatic capability The approach advocated by Hoover Perez and Hendry Krolzig consists in exploring a limited number of paths starting from each initially non significant variable and performing thereafter the successive elimination of the less significant variables provided that the model passes well chosen specification tests This approach will lead at the end to a few models which can then be chosen by encompassing tests or if this is not sufficient to obtain only one model by an information criterion such as the Akatke s one The exploration of several paths and the use of specifications tests cover against the risk of eliminating a relevant variable but only the more relevant paths are indeed explored Hendry and Krozlig Monte Carlo simulations show that this method leads indeed to very satisfactory results the average inclusion rate of a non relevant variable can be set at a low level while retaining significant power The corresponding algorithm summed up in figure 3 is implemented by Grocer function automatic which is as far as I know the only econometric package today to provide this very useful device except for pc gets the commercial package built by Hendry and Krolzig From a programming point of view the following features are noteworthy e the function involves several loops
19. rst it is free and therefore portable a feature that is not guaranteed with any commercial package since none of these has become a standard for the profession Econome tricians working on different institutions are therefore not always able to exchange pieces of works which they can do with Siclab Similarly an econometrician using Scilab who changes her working location will have no problem reusing her programs Second Scilab is very similar to Gauss or Matlab these software are used a lot by econo metricians in particular those who develop new methods It is matrix oriented and contains a robust numerical optimisation program econometrics deals basically with matrices and many econometric problems involve likelihood maximisation And many programs implementing use ful econometric applications written in Gauss or Matlab are available on the web around half functions that compose Grocer have been built by translating such programs Third unlike Gauss or Matlab Scilab allows a user to create her own data types through the typed list tlist capability this feature has proved very useful to create the time series type of frequent use in a very lively branch of econometrics 2 Grocer philosophy through the example of ordinary least squares The reader familiar with Scilab may be aware of a Scilab function called leastsq that performs ordinary least squares Grocer contains a function called ols devoted also to ordinary least squares The
20. s called the data generating process When a data generating process DGP involves a small number of variables among a much bigger set of potentially important variables then a researcher who wants to recover the true model among all the linear models than can be built from this data set faces the following difficulties e if she wants to estimate all models that can be built from this data set then the cost of search will generally be prohibitive if there are n variables in the initial set then there are 2 potential models e if she uses a top down method based upon the successive elimination by the mean of a testing procedure based for instance on the successive elimination of the variable with the lowest Student T then the number of models to estimate is more limited at most n but the risk of not finding the best model is great if she chooses a relatively loose significance level then she risks retaining erroneous variables since as emphasised by Hendry and 14 Krolzig 2000 type I errors are known to accumulate if she chooses to protect herself against such a risk with a high significance level she then risks missing some relevant variables and the bigger is the colinearity between variables the bigger is this risk So estimating a relevant econometric model generally involves a lot of time and skill Re cently Hoover and Perez 1999 with further refinement by Hendry and Krozlig 2000 have however proposed a com
21. stageO test_func set of specification ip tests aldfO stage0 model yes test if this is final model ni for all non significant variables auto_stage1 set of specification tests stage 1 models yes test if there is one and only one stage 1 model n build the union model and calculate the number of models that are accepted against this model Ip or more than 1 continued on next page only one 17 stage 2 estimation for all non significant variables of the union model auto_stage1 stage 1 models one and only one stage 1 model yes test if there is no v build the union model and calculate the number only one of models that are accepted against this model 0 more than 1 select the union model select the model according to an information criterium v vyv v v v i THIS MODEL IS THE FINAL MODEL printmat _ prtuniv prtauto_univ hacen prtauto es prtauto_multi e a results tlist containing the ols results tlists of various estimated model the way the final model was obtained the paths followed in stages 1 and if any 2 Legend function name of a Grocer function set of Grocer functions intermediate results intermediate results in the function automatic output output from the function automatic input input of the function au
22. t in the re gression this boolean is used by the printing function to determinate if the R must be printed or not rols rsqr R rols rbar R rols f F stat for the nullity of coefficients other than the constant rols pvaluef its significance level rols prests boolean indicating the presence or absence of a time series in the regression this boolean is used by the printing function to determinate if the bounds must be printed or not rols namey name of the y variable rols namex name of the x variables rols bounds if there is a time series in the regression the bounds of the regression rols like log likelihood of the regression 10 Figure 2 Hendry and Ericsson 1991 preferred equation A m p 0 69Ap 0 17A m p y 0 630R 0 14 0 06 0 053 0 093 m p y 0 023 0 008 0 004 6 T 100 1964 3 1989 2 R 0 76 1313 DW 2 18 Normality y 2 1 53 AR 1 4 F 4 91 1 94 ARCH 1 4 F 4 87 0 74 X F 8 86 1 36 fa X X F 14 80 1 05 RESET F 1 94 0 08 2 6 An example Hendry and Ericsson 1991 US money demand In a famous paper Hendry and Ericsson 1991 have estimated a US money demand that respected all canons of applied econometrics Results of their preferred specification as they were published in their paper are reported in Figure 2 Retrieving their results in grocer involves the following comm
23. the estimation of the coefficients and the calculation of all these statistics Once the estimation is done she should check the validity and robustness of these results This task involves the application of specification tests such as tests of stability of the coefficients so called Chow test or CUSUM test tests of homoskedasticty the most famous of these tests is called the White test but there are many other useful tests Most of these specification tests imply auxiliary regressions of the residuals on various exogenous variables Some tests such as the CUSUM test is usually represented graphically Lastly econometricians frequently use data in the form of time series that is vectors of real data associated with dates such as quarterly GDP monthly inflation Therefore many econo metric software allow the user to manipulate directly such objects Important exceptions are Matlab and Gauss which do not include or even allow to create such objects Grocer function ols allows to deal with time series implemented in Grocer through Scilab tlist capability and contrary to many software ols is sufficiently flexible to allow to deal both with matrices and time series 2 2 ols architecture ols architecture which is summed up in figure 1 derives largely from the objectives previ ously described e the flexibility as regards the authorised inputs obliges to transform them into matrices this is done by Grocer functions explox and e
24. tomatic instruction a intermediate computation in automatic function 18 gt rman automatic gyman lagts gyman lagts 2 gyman lagts 3 gyman gt ypa_m1 ypa_mi lagts ypa_m3 lagts ypa_m3 lagts ypa_m2 gt lagts ypa_m2 lagts ypa_m1 lagts ypa_m1 lagts 2 ypa_m3 gt ppy_m1 ppy_m1 lagts ppy_m3 lagts ppy_m3 lagts ppy_m2 gt lagts ppy_m2 lagts ppy_m1 lagts ppy_m1 lagts 2 ppy_m3 gt ccg_m1 ccg_mi lagts ccg_m3 lagts ccg_m3 lagts ccg_m2 gt lagts ccg_m2 lagts ccg_m1 lagts ccg_m1 lagts 2 ccg_m3 gt sto_ml sto_mi lagts sto_m3 lagts sto_m3 lagts sto_m2 gt lagts sto_m2 lagts sto_m1 lagts sto_m1 lagts 2 sto_m3 gt cte prt final test And Grocer results were the following final model ending reason stage 2 models selected by bic criterion ols estimation results for dependent variable gyman estimation period 1979q2 2002q4 number of observations 95 number of variables 4 R72 0 4970310 ajusted R 2 0 4804496 Overall F test F 3 91 29 975222 p value 1 439D 13 standard error of the regression 0 8614509 sum of squared residuals 67 530894 DW 0 2 2836444 Belsley Kuh Welsch Condition index 13 variable coeff t statistic p value lagts ccg_m3 lagts ccg_m2 0 0845522 2 9341329 0 0042328 More y
25. ts In order to use the good variable local variables created before any evstr existing in a Grocer function are prefixed by grocer_ and the user is recommended not to prefix her variables by grocer_ The transformation of input variables into matrices is basically done by the two functions explox and exploy which are called in function explouniv for all the univariate methods which were presented at the end of part 3 2 These functions perform the following tasks which imply a battery of conditional operations and computations 2 5 determine the type of the input variables for the variables whose type is string store the string into the vector of names that will be used for subsequent display and thereafter recover the corresponding variables for other types of variables define the name by a default name provided as an input of the function when called from ols or another univariate function the default name is exogenous suffixed by the place of the corresponding variable in the list of variables if the user has provided time bounds then for the variables whose type is time series recover the values of the time series over the specified time period if the user has not provided time bounds then create for the first encoutered time series or update for the other time series the admissible time bounds only when the time bounds are determined then recover the values of all time series over the specified
26. use also the explox and exploy functions The results of all these functions are also displayed by the function prtuniv or graphed by the function pltuniv And the output of almost all these functions takes the form of a tlist that can be used as input of any function computing a specification test 2 3 Grocer time series As mentioned above a time series is a vector of real values associated with dates In Grocer this is implemented as a typed list tlist tlists are lists whose first argument is a string vector where the first argument of this vector is its type and the other ones the names of the subsequent fields So time series have been built as tlists with type ts and includes three fields freq dates and series myts freq is the frequency of the time series a value of 1 resp 4 or 12 indicates that myts is an annual time series resp quarterly or monthly other frequencies are also allowed myts series is the vector of values myts dates represents the time period of myts they are numerical values to allow more convenience when executing operations addition multiplication on time series see below Grocer function reshape allows to create a time series from a real vector and a starting date Take for instance time series myts created by the following command gt myts reshape 2 1 1 4 3 2 4 5 1 5 04q1 then the fields take the following values gt myts freq
27. ween brackets under each coefficients the corresponding standard errors they can be recovered by the following commands gt rhe beta rhe tstat ans 0 1254099 0 0580064 0 0601704 0 0085397 0 0040279 Some slight differences appear with Hendry and Ericsson figures however the re estimation of this model by Hendry and Krolzig 2000 leads to the same Student statistics as Grocer ones The following statistics presented by Hendry and Ericsson can be found on the estimation display their R 0 76 their 0 13 called in Grocer standard error of the regression their DW 2 18 called in Grocer DW 0 To recover the results of their specification tests it is now necessary to run the corresponding Grocer functions with the results tlist that has been named rhe as an input gt arlm rhe 4 12 Lagrange multiplier 1 4 autocorrelation test chi2 4 7 1563181 p value 0 1278545 Lagrange multiplier 1 4 autocorrelation test F 4 91 1 941783 p value 00 1102067 this is what Hendry and Ericsson call AR 1 4 gt archz rhe 4 ARCH test chi2 4 2 8467913 p value 0 5837830 ARCH test F 4 87 0 7357736 p value 0 5700480 this is what Hendry and Ericsson call ARCH 1 4 gt namexbp rhe namex bpagan rhe namexbp 1 4 namexbp 1 4 2 Breusch and Pagan heteroscedasticity test F 8 86 1 3572821 p value 0 2267534 this is
28. what Hendry and Ericsson call X note that the test does not exits as such in Grocer but that it is an example of a more general test called Breusch and Pagan test that has been programmed in Grocer So Hendry and Ericsson test can be recovered although in a more complicated manner than with other tests 4 gt white rhe warning matrix is close to singular or badly scaled rcond 1 0425D 08 White heteroscedasticity test chi2 14 15 475464 Writing this article led me to discover 2 slight bugs in the function bpagan they have been corrected and the correction posted on Grocer web site 13 p value 0 3464440 White heteroscedasticity test F 14 80 1 0462196 p value 0 4180710 this is what Hendry and Ericsson call X X gt reset rhe 2 power 2 non linearity RESET test F 1 94 0 0821074 p value 0 7750922 this is what is called by Hendry and Ericsson RESET gt doornhans rhe Doornik and Hansen normality test chi2 2 1 9768209 p value 0 3721678 This is another more recent normality test than the one used by Hendry and Ericsson hence the slightly different numerical results but the conclusion remains unmodified at standard significance levels the normality hypothesis is not rejected 3 The function automatic An applied econometrician often aims at recovering the economic model that has generated the data set she has at her disposal this model is what i
29. wo and three stage least squares have been implemented along with many up to date VAR methods Vector Autoregressions Vector Error Correction Models Bayesian Vector Auroregressions Im pulse Response Functions can be calculated and graphed for each of these methods For more details about all econometric functions available in Grocer the interested reader should refer to Grocer user manual see Dubois 2004 The aim of this paper is not however to provide a comprehensive description of these procedures but rather to provide an insight on how they have been implemented in Scilab and present more deeply one of the two features that make Grocer original with respect to existing econometric packages an automatic function that selects the best model from a set of numerous potentially relevant variables the other not presented in the paper being a set of functions calculating the contributions of exogenous variables to an endogenous one for any dynamic equation Part 1 quickly presents the characteristics of Scilab that makes it attractive to an econo metrician Part 2 illustrates Grocer philosophy through the example of ordinary least squares Part 3 presents the automatic function that selects the best model from a set of numerous potentially relevant variables Part 4 concludes 1 Scilab attractiveness for an econometrician Scilab offers many attractive features for an econometrician Three of them are particularly important Fi
30. xploy both are at the basis of all high level Grocer functions that are as flexible as ols with respect to the inputs cf part 2 4 e the possibility to apply ols to time series comes trough the creation of a tlist of type ts this in turn has obliged to write the overloading functions allowing to perform usual operations with time series as well as new specific functions useful for the manipulation of time series cf part 2 3 e there is a low level function called ols2 that applies to the objects that appear in the formula that is a vector Y and a matrix X e further calculations require a lot of intermediate results For instance the computation of some specification tests requires the vector of residuals the number of variables the matrix of exogenous variables the period of estimation for time series the names of exogenous variables So the output of ols function is a tlist whose type is results in that case the resort to a tlist is just for the sake of collecting all results without using the overloading feature associated with tlists e the printing of the results is made by a specialised function called prtuniv this function takes the results tlist from ols as input if the results tlist is present in the environment then it can be printed again without resorting to a reestimation of the model as many Grocer functions that display results on screen this function uses a very simple function calle
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