Seasonal Cointegration Analysis: Example of South Africa

Abstract

In this paper, unit root tests and cointegration analysis is discussed with South Africa economic data for the period 1990:01-2013:04. HEGY and periodogram methods were used for unit root tests. Time series has a seasonal unit root result of HEGY and periodogram methods. Cointegration analysis was applied with Engle-Granger and periodogram methods. A comparison is made between the HEGY, the periodogram and the Engle-Granger methods results. Therefore the three methods have been prefered in order to test the unit root and cointegration. 

Keywords

• Time series,Seasonal unit root,HEGY method,Cointegration,Engle- Granger method,periodogram method

Mevsimsel Kointegrasyon Analizi: Güney Afrika Örneği

Abstract

Bu çalışmada 1990:01-2013:04 dönemi Güney Afrika ekonomik verileri için birim kök testleri ve kointegrasyon analizi tartışılmıştır. Birim kök testleri için, HEGY ve periodogram yöntemleri kullanılmıştır. HEGY ve periodogram mevsimsel birim kök testleri sonuçlarına göre zaman serilerde mevsimsel birim kök olduğu tespit edilmiştir. Kointegrasyon analizi ise Engle-Granger ve periodogram yöntemleriyle uygulanmıştır. Bu çalışmada HEGY, periodogram ve EngleGranger yöntemleri ile elde edilen bulgular karşılaştırılmaktadır. Bundan dolayı, bu üç yöntem birim kökü ve kointegrasyonu test etmek amacıyla tercih edilmiştir. 

Keywords

• Zaman Serileri,Mevsimsel birim kök,HEGY yöntemi,Kointegrasyon,EngleGranger yöntemi,periodogram yöntemi

References

1. Akdi, Y. (2010), “Zaman Serileri Analizi (Birim Kökler ve Kointegrasyon)” 2. Baskı, Gazi Kitabevi.
2. Akdi, Y. (1995), “Periodogram Analysis for Unit Roots”, Ph.D. Thesis, North Carolina State University.
3. Akdi, Y. and Dickey, D. A. (1999), “Periodograms for Seasonal Time Series With a Unit Root”, İstatistik, Journal of the Turkish Statistical Association, 2, 3, 153-164.
4. Akter, R. and Majumder, A. K. (2013), “Restricted Testing Procedure and Modified Dickey- Fuller Test”, Research Journal of Mathematical and Statistical Sciences 1, 17-20.
5. Berument, H., Akdi, Y. and Atakan, C. (2005), An Empirical Analysis of Istanbul Stock Exchange Sub- İndexes, Studies in Non linear Dynamics & Econometrics Electronic Press, 9, 3.
6. Dickey, D. A. (1976), “Estimation and Hypothesis Testing in Nonstationary Time Series”, Unpublished, Ph. D. Dissertation,Iowa State University.
7. Dickey, D. A. and Fuller, W. A. (1979), “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”, Journal of the American Statistical Association, 74, 427- 431.
8. Engle, R. F., ve C. W. J. Granger (1987), “Cointegration and Error Correction: Representation, Estimation and Testing”, Econometrica, vol:55, 251-276.

9. Franses, P. H. And Hobjin, B. (1997), “Critical Values for Unit Root Tests in Seasonal Time Series”, Journal of Applied Statistics, 24, 1, 25-47.
10. FRED: Federal Reserve Economic Data, https://research.stlouisfed.org/fred2.
11. Ghysels, E., Lee, H. S. and Noh, J. (1994), “Testing for Unit Roots in Seasonal Time Series”, Journal of Econometrics, 62, 415 – 442. Princeton New Jersey.
12. Gürel, S. P. And Tiryakioğlu, M. (2012), “Seasonal Unit Root: An Application to Turkish Industrial Production Series”, Business and Economics Research Journal, 3, 4, 77-89.
13. Harris, R. and Sollis, R. (2003), “Applied Time Series Modellind and Forecasting”, John Wiley& Sons.
14. Hylleberg, S., Engle, R. F., Granger, C. W. J. and Yoo, B. S. (1990), “Seasonal Integration and Cointegration”, Journal of Econometrics, 44, 215-238.
15. Sevüktekin, M. ve Nargeleçekenler, M. (2010), “Ekonometrik Zaman Serileri Analizi, Eviews Uygulamalı”, 3. Baskı, Nobel Yayın Dağıtım.
16. Shirvani, H. , Wilbratte, B., Delcoure, N. (2009), “Testing for Periodic Integration and Cointegration of the Stock Prices of the G7 Countries”, Investment Management and Financial Innovations,6,1.
17. Tıraşoğlu, M. (2012), HEGY Mevsimsel Birim Kök Testi: Türkiye’de TÜFE ve TÜFE Harcama Grupları için bir Uygulama, Kırklareli Üniversitesi İ. İ. B. F. Dergisi.
18. Wei, W. W. S. (2006), “Time Series Analysis Univariate and Multivariate Methods”, Second Edition, Pearson-Addison Wesley.