Michiel Helder and Marielle C.T.A Geurts. Hoofdkantoor PTT Post / Dutch Postal Services Headquarters

Transcription

1 SHORT TERM PREDICTIONS A MONITORING SYSTEM by Michiel Helder and Marielle C.T.A Geurs Hoofdkanoor PTT Pos / Duch Posal Services Headquarers Keywords macro ime series shor erm predicions ARIMA-models faciliy 1. Inroducion In many organisaions here is a grea need for regular informaion abou he near fuure. One of he mehods o obain his informaion is o use shor erm predicions. A well known mehod of producing shor erm predicions is he mehod of Box and Jenkins (ARIMA-models). Every monh when new daa ge available a daase of he ime series is presened o acualize he shor erm predicions. Because some of he mos recen hisorical daa may have changed his daase conains no only he new realizaions bu conains also informaion abou he pas. To do he acualizaion of he predicions in a correc way several checks have o be done. This checking akes a lo of ime especially when here is a large number of ime series. To reduce he amoun of ime spen on he updaing of he predicions a monioring sysem has been developed he Shor Term Predicions (STP) Monioring Sysem an applicaion wrien in he SAS sofware. The idea of he STP-Monioring Sysem is ha he user reviews only hose ime series ha have o be reviewed. In pracice only a small number of ime series have o be reviewed and he ime spen on he updaing is reduced remendeously. 2. Shor Term Predicions Monioring Sysem When new daa ge available o produce new forecass he user has o ake wo acions before producing forecass compare he new daa o he daa used in he previous period chec if he model used in he previous period is sill valid. To reduce. he ime spen on his checking a monioring sysem wrien in he SAS Macro language..has been developed he Shor Term Predicions (STP) Monioring Sysem. The Sysem no only checks he ime series i also generaes he forecass auomaically

2 r. If some aspecs of he daa or he model have changed. he Monioring Sysem wries a message o a monior file o enable he user o ake he appropriae acion. On he oher hand. if for a paricular ime series he daa have no changed and he model is sill valid. no message will be wrien o his monior file. Thus. he user will have o review only hose ime series of which informaion has been wrien down o he monior file. The STP Monioring Sysem is divided ino four sub-programs he daa checking.program (chaper 4) he esimaion and forecasing program (chaper 5) he reconciliaion and oupu program (chaper 6) he updaing program (chaper 7) Each of he programs will be considered in he nex secions of his paper. 3. Pre-requiremens of he STP Monioring sysem '_. '. Before using he STP Monioring Sysem he user has o have he following informaion available in SAS daases hisorical informaion of he ime series ARIMA modelspecificaion of he ime series The hisorical daa will be used in he daa checking program while he ARIMA model will be used in he esimaion and. forecasing programs. I ; f.. } { r f E Ii ;.. -'. r.;_ - Y' (. (. I' ' r. I!. R Daa checking. program '-. The firs program of he mohioing syse is he daa checking program. In his program he new daa will be. compared o he da.a used in he previous period. The reason for his is. ha if here are changes in he daa. hese can affec he. esimaioq of he model and will evenually give wrong forecass... '.'. To compare he wo aases i is necessary o read he new daa ino a SAS-daase.The old daase is already a SAS-daase creaed in he previous.period. 537

3 Figure 1 a floaing char'of he daa checking program monhly daa period -1 monhly daa period acualized daa daa monior file ime series analysis program Afer having merged boh daases he new daase will go ino he daamonior. In he daa-monior he following aspecs wil be esed are here any differences in he realisaions of he old and he new daa? If here are diff'erences beween he daa used in previous period and he. acual period he daa have o be adjused. does henumher of he new realisaions compared o he daa used in he previous analysis differ from one? If he number is zero a new analysis will no be necessary; if he number is larger han one here. is a greaer chance ha he modelspecificaion will have o be changeq. are he new realisaions ouliers compared o he forecass of he previous analysis? To check his he 95% upper and lower bounds of he forecass of he previous periods are used. If he answer o any of hese hree quesions is yes a message will be wrien down o he monior-daase and he user can ake appropriae acion. The mos commom messages ha are wrien down o he monior-daase are adminisraive correcions; e.g insead of incorrec daa-enries e.g insead of changes of scale e.g. 2.0 insead of 1988 If all hree quesions are answered in he negaive no message is wrien o he monior-daase and he daa are ready for he nex program. 5 Esimaing- and forecasing-program Afer he daa.have.been checked he acual' daa are re.ady for he esimaing- and forecasing-program. In his program he acual daase will be colmeced o.he daase conaining. he informaion.abou he model specificaion. This informaion is soredin a SAS daase. 538

4 . Figure 2 a floaing char of he esimaing and forecasing program ime series analysis PROC ARIMA model specificaion forecas monior reconciliaion and oupu program. f $ fc..' 'i... b'. ( k ( Z i F. k. ; R. f i. The following aspecs of he modelspecificaion is sored in he SASdaase idenificaionnumber of he ime series ile of he ime series period of he firs observaion of he ime series logarihm-ransforl!laion (yes/no) correcion for he number of days (yes/no) cumulaive ime series (yes/no) AR-parameers MA-parameers period of differencing inervenion-analysis (yes/r.o) which inervenions?. This informaion abou he modelspecificaion of a paricular ime series will be conneced o he STP Monioring Sysem as macro-variables hrough he CALL SYMPUT saemen. These macro-variables conaining he informaion of he modelspecificaion can be used everywhere wihin he macro-program. These macj;'o-variables are used in he PROC ARIMA-saemen. Before calling he ARIMA-procedure he daa have o be ransformed according o he modelspecificaion (logarihm-ransformaion or correcion for he numbers of days). Afer he ransformaion of he ime series he nex hing o deermine is he way in which he ARIMA procedure is execued. Therefore he ARIMAsaemen conains some macro-variables ha are solved according o he informaion in he modelspecificaion. Furhermore.he number of predicions has o be deermined he predicion horizon. 539

5 The ARIMA-procedure used in he STP-Monioring Sysem conains he following saemens PROC ARIMA DATA=daasename; IDENTIFY VAR=&name of he ime series(&perlod of differencing) CROSSCOR=(&inervenions) NOPRINT; ESTIMATE P=&AR-parameers Q=&MA-parameers &inercep INPUT=(&inervenions) PLOT MAXIT=150 METHOD=ML PRINT; FORECAST LEAD=&predicion horizon OUT=daasename; where he SAS macro variables are denoed by a &. When all SAS macro variables in he ARIMA saemen are replaced by heir values he ARIMA-procedure will be execued. The ARIMA-procedure only generaes an oupu daase of he predicions heir 95%-confidence inervals and he sandard errors of he predicions. To allow he user o check wheher he model is sill valid his informaion in he sandard ARIMA-oupu daase is no sufficien. I is necessary o ge he informaion available ha has been generaed o he SAS-oupu window. Therefore he ARIMA-oupu is wrien o an exernal file and he necessary informaion is read from his exernal file ino he STP-sysem. The following saisics are sored ino a SAS-daase esimaes of he parameers and heir -values correlaion-marix of he esimaed parameers auocorrelaion-funcion parial auocorrelaion-funcion chi-squares value of he consan erm esimaed variance and sandard deviaion of he model This informaion enables he user o check if he modelspecificaion is sill valid or has o be reviewed. This checking is done in he esimaionmonior a collecion of ess concerning he esimaion of oe model. The following ess are par of he esimaion-monior.' ) ' i -.. l es of significance of he esimaes of he parameers es of correlai'dn beween he esimaed parameers es o compare he esimaed sandard error in his period wih he sandard error in he previous period es of significan auocorrelaion coefficiens es of significan parial auocorrelaion coefficiens es of he chi-squares es o deermine if here is a srucural break in he ime serie Messages are only wrien o he monior daase if' aily of he ess is answered affirmaively. If for some ime series messages have been wrien o he monior-daase he user will have o deermine wheher he model specificaions.have o be changed or no. If he modelspecificaion has o be changed an FSEDIT-screen is provided o change he model and he esimaion-monior has o be execued again for his ime series. Afer he esimaion-monior has been execued and no messages are generaed he forecass will have o be checked on heir qualiy. Therefore a hird monior is aken ino accoun he forecas-monior. This monior conains a number of ess o examine he forecass. The following ess are par of he forecas-monior es of ouliers in he forecass es of normaliy of he residuals es of' forecas-bias es of he mean predicion error (MPE). 540

6 As in he daa and esimaion-monior informaion will be wrien o he monior daase only if here is a reason o do so. If here are no messages he esimaion and forecasing-program is almos finished and he forecass are produced. In he case he original ime series is ransformed he forecass have o be re-ransformed o ge forecass of he original ime series (logarihm correcion or correcion for he number of days).. 6. Reconcilaion- and oupu-program Alhough he forecass are produced and sored in a SAS...daase he updaing of he predicions has no ye finished. Because he program is wrien as a SAS-macro program and each macro call generaes he predicion of one paricular ime series he predicions are independen. of one anoher. Bu in pracice someimes here may be relaions or sumresricions beween he ime series. In he case of regional and naional daa he sum of he regional daa on he one side and he naional daa on he oher side will have o have he same value. For he realised daa his condiion may be righ bu for he forecass his may no be he case because he forecass are produced independen of each oher. '! To fulfill his condiion on he forecass a reconcile acion is carried ou. Therefore he ulimae forecass are weighed; he variances are he weighing facors. In his way he linear relaions or sum-resricions are brough ino he' forecass. Afer his reconcile acion has aken place he predicions can be wrien away in a forma chosen by he user and he process of producing new acual forecass has been compleed. ;. '. r ;..' Ie f I ' I' (; ' 1!.7. Updae-program Alhough he producion of he forecass has finished here is sill one small aspec o be looked a. To riil he STP-program in he nex period he sysem has o be updaed. The hisorical daases have o be replaced by he acual daases of his period. This acion is carried ou by he updae-program. 8. SAS;producs necessary for he STP-Monioring sysem ;. To run he STP-program he user needs he following SAS-producs SAS-Base SAS-ETS SAS-FSP SAS-IML f e' i.. I ' TheSAS-baseproduc is'needed o run hesas-sysem. This produc enables 'he user o do he daa-manipulaions. I also allows he sysem o work wih he SAS-macro language. To produce he forecass wih he ARIMAprocedure i is necessary o have he ETS-module. Furhermore o change he daa..; and he modelspecificaions i is necessary o have he FSPmodule (PROC FSEDIT). Finally in he esimaion-monior some programming is done wih he IML-module o perform marix-operaions. 541

7 9. Performance of he STP-Monioring Sysem A his momen he STP-program is available in a TSO/MVS-environmen on he IBM-mainframe and in a MS-DOS-environmen on an IBM-compaible pc. On he IBM-mainframe he SAS configuraion is he version while on he pc he 6.03 vesion of he SAS sysem is used. Because of he Muli Vendor Archiecure (MVA) of he SAS sysem he differences beween he wo STPversions are limied. However one difference in a SAS-procedure beween he wo SAS versions has been noified The UNIVARIATE-procedure o es normaliy of he residuals uses in he 5.18-mainfrane version he KOLMOGOROV-SMIRNOV es if he number of observaions is larger han 50 while in his case he SHAPIRO--WILK es is used in version The performance of he STP-Monioring Sysem on he IBM PS2 model 80 is accepable o he users. Wihou echnical improvemens he sysem uses 12 minues o execue one ime series. To improve he performance of he STP Monioring sysem some improvemens have been made. Using a mahemaical co-processor disk-caching and expanded memory did improve he performance of he STP-Monioring Sysem o 4.5 minues. 10. Conclusion The STP-Monioring Sysem gives he user he possibiliy o produce he forecass of' a large number of ime series auomaically and a he same ime reduces he ime spen on producing high qualiy forecass. No useless checking has o be done by he user and he aenion can be focused on he quali y of he forecas s. The larger he number of ime series o be prediced he larger he gains of he STP-Monioring Sysem. In pracice a he ime spen on producing forecass is reduced by 90%. For addiional informaion conac Michiel Held.er PTT Pos BV Informaie Manegemen Pos PO Box GG The Hague The Neherlands