TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME

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1 TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME RADMILA KOCURKOVÁ Sileian Univerity in Opava School of Buine Adminitration in Karviná Department of Mathematical Method in Economic Czech Republic Tel.: Fax: [email protected] Key Word: time erie analyi, proce ARIMA, unemployment, programme SPSS Introduction In my lecture I would like to tell you omething about the time erie, repectively about trend in the number of job applicant regitered by labour office in the Czech Republic. On the bai of reult I will forecat the number of job applicant regitered by labour office till December My data wa taken from tatitic ource: Minitry of Labour and Social Affair. At our univerity I teach the coure Time Serie Analyi for the tudent of ytem engineering and information pecialiation. The main aim of thi ubject i: invetigation of the regular coure of time erie; deviation invetigation of expected regularity; prediction of the future time erie; regular determination of the convenient control direction for influence of time erie. During the leon I uually ue MS Excel and tatitic programme SPSS (Statitical Package for the Social Science). SPSS make ome operation with the time erie poible in the baic module Bae; for deeper analyi it i neceary to join module Trend. For SPSS programme i the time erie normal data file and it i preuppoed that one row of the date nut contain the obervation in one time and the row ground in the way, that the oldet obervation i the firt, the younget obervation i the lat row of the nut. 836 Time erie analyi Firtly, we have to decribe the trend of time erie of the applicant regitered by labour office in the Czech Republic. From the Graph 1 we can ay that January 1997 the number of job applicant grow much more than in the previou year. Thi time erie i not tationary (which can be deleted by the eaonal difference of the time erie).

2 Theory Trend and prediction of time erie can be computed by uing ARIMA model. ARIMA (p,d,q) model i complex a linear model. There are three part (they do not have to contain alway all of thee): AR (Autoregreive) linear combination of the influence of previou value; I (Integrative) random walk; MA (Moving average) linear combination of previou error. Thee model are very flexible, quite hard for computing and for the undertanding of the reult. They are demand quality and a large number of dealing date (it i aumpted at leat 50 dealing or obervation). Graph 1 Trend in the number of job applicant regitered by the labour office: January 1990 January The number of job applicant DEC 1999 MAY 1999 OCT 1998 MAR 1998 AUG 1997 JAN 1997 JUN 1996 NOV 1995 APR 1995 SEP 1994 FEB 1994 JUL 1993 DEC 1992 MAY 1992 OCT 1991 MAR 1991 AUG 1990 JAN 1990 Source: Minitry of Labour and Social Affair At firt, we have to identify the type of the model and the value of the parameter. We can do it by uing autocorelate (ACF) and partial autocorelation (PACF) function of the tationary time erie. Autocorelate mean the correlation between time erie and the ame time erie lag. Partial autocorrelation are alo correlation coefficient between the baic time erie and the ame time erie lag and we will eliminate the influence of the member between. Thi coefficient preent only about direct tructure, for example between y t and y t!2 with the elimination of tranmiion over the obervation y t! 1. In output of SPSS we compute ignitication for the individual parameter in ARIMA model. From thee value we can determine if the parameter can be ued in thi model or not. In the cae of computing more model we chooe the model where AIC (Akai information criteria), repectively SBC (Schwartz-Baye criteria) are minimal and Log likelihood i maximal. At the end we verify if the reidual component i the white noie. In ARIMA model, we aume dependence between the quantitie y, y, y, y, y,... t! 2 t! 1 t t " 1 t! 2 837

3 If thi proce contain the eaonal fluctuation, a it i in thi model, we can expect alo the dependence eaon: yt! 2, yt!, yt, yt ", yt! 2,..., where i the length of the period (in thi cae 12). p q d P Q D Thi proce i called SARIMA (p,d,q) (P,D,Q), where i order of proce AR, i the order of proce MA, i the order of difference, i order of eaonal proce AR, i the order of MA, i order of eaonal difference, i the length of eaonal period. The equation of thi model i: ) # B $ ( # B$#! B$ # 1! B $ yt ' & q # B$ % Q # B $ a t # B$ ( p i autoregreive operator, & q# B$ P # B $ # B $ i the operator of moving average, ) i eaonal autoregreive operator, % i eaonal operator of moving average, Q * a t + i white noie. P p d D 1, where Practice For the fit we have to etimate the parameter of the model by uing autocorrelation and partial autocorrelation function. Becaue time erie i not tationary we have to differentiate it, by the firt order. We alo aume the eaon dynamic that i why we differentiate time erie alo by eaonal fit order. Graph 2, 3 Autocorrelation and partial autocorrelation function time erie of the number of job applicant 1,0 1,0,5,5 0 0 ACF -,5-1, Partial ACF -,5-1, Confidence Limit Coef ficient Lag Number Source: own calculation 838 Tranform: difference (1), eaonal difference (1, period 12)

4 On the bai of the form function we chooe model SARIMA (1,1,0) (1,1,0) 12 or model SARIMA (1,1,0) (1,0) 12. Akai information criteria and Schwartz-Baye criteria are lower at the model SARIMA (1,1,0) (1,1,0) 12, we chooe thi model. The horter SPSS output for model SARIMA (1,1,0) (1,1,0) 12 Variable: The number of unemployment applicant Regreor: NONE Non-eaonal differencing: 1 Seaonal differencing: 1 Length of Seaonal Cycle: 12 No miing data. FINAL PARAMETERS: Number of reidual 108 Standard error Log likelihood -1072,8442 AIC 2149,6884 SBC 2155,0526 Variable in the Model: B SEB T-RATIO APPROX. PROB. AR1, , ,285775, SAR1 -, , ,810591, new cae have been added B B 1 B B y t a. General equation of the choen model i: ) # $ ( # $#! $ #! $ ' t After the modification of the equation and ubtitution of etimated value, we get the following equation and it decribe the dynamic of our time erie: y t 184, y 1 84y 57y 11, y 48y 43y 79y 84y ' t!! t! 2 " t! 12! t! 13 " t! 14 " t! 24! t! 25! t! 26 " a t We can ay, that the number of job applicant thi month i much more influenced by the number of job applicant in the lat month. 839

5 Réumé We can decribe graphically the original time erie of the number of job applicant and the predicted time erie by SARIMA (1,1,0) (1,1,0) 12. Graph 4 The original and etimation value of the number of job applicant The number of job applicant JUL 2000 DEC 1999 MAY 1999 OCT 1998 MAR 1998 AUG 1997 JAN 1997 JUN 1996 NOV 1995 APR 1995 SEP 1994 FEB 1994 JUL 1993 DEC 1992 MAY 1992 OCT 1991 MAR 1991 AUG 1990 JAN 1990 Original time erie Etimation Source: own calculation Table 1 how forecating the time erie in the number of job applicant regitered by labour office in the Czech Republic. Table 1 Expected number of job applicant in year 2000 Month The number of job applicant February March April May June July Augut September October November December Source: own calculation 840

6 In year 2000 we can expect the highet the number of job of applicant in December 573, 290. In comparion with the ame period of year 1999 the number of job of applicant ha extended by about 85, 667 applicant. The lowet number of job applicant we can expect in May 2000 and that i 495, 024. Thi i the conequence of the eaonal unemployment. In thi period, there are ome job for contruction worker, agriculture worker, and young people will go abroad for a job. Graph 5 Expected monthly addition of the number of job applicant in year Expected monthly addition February March April May June July Augut September October November December Source: own calculation In year 2000 we can expect the highet addition number of job applicant in December around 22, 125, July around 21, 392 (in thi period graduated tudent from every chool are regitered by labour office). The lowet number of job applicant we can expect in April 2000 around and in October 3, 650 applicant. Summary The unemployment i a big problem for almot every country. That i way I decided to ue SPSS oftware for the analyi of thi problem in the condition of the Czech Republic. After the Velvet revolution, the Czech Republic ha the problem with unemployment, epecially in it three previou year. Very dangerou i the ituation in ome place in the Czech Republic, where indutry wa the main ector of employment. School of Buine Adminitration i in one of uch part country (Karviná) and there i about 69.4 applicant to one work place. Literature NORUŠIC, M. J. SPSS Profeional Statitic 7.5. Chicago: SPSS Inc., ISBN SPSS INC. SPSS Trend 6.1. Chicago: SPSS Inc., ISBN DORNBUSCH, R., FISCHER, S. Makroekonomie. Praha: SPN, ISBN