• ISSN: 2148-2225 (online)

Ulaştırma ve Lojistik Kongreleri

alphanumeric journal

The Journal of Operations Research, Statistics, Econometrics and Management Information Systems

Comparison of Cointegration Tests for Near Integrated Time Series Data with Structural Break

Esin Firuzan, Ph.D.

Berhan Çoban


Abstract

Sample size of data, presence of structural break, location and magnitude of potential break, and having with near integrated process might affect the performance of cointegration tests. Engle-Granger (EG) and Johansen Cointegration tests may have erroneous results since they do not take into account possible structural break unlike Gregory – Hansen (GH) cointegration test. In this study, it is argued that the suitable choice of cointegration tests is quite complex, since outcomes of these tests are very sensitive to specifying these properties. The performance of cointegration tests is compared to each other underlying properties. This study presents how standard residual based tests- Engle-Granger and Gregory-Hansen- for cointegration can be implemented if series is near integrated, that is close to a unit root process. For assessing the finite sample performance of these tests, a Monte-Carlo experiment showed that both cointegration tests have relatively better size and power properties depend on break point, break magnitude, sample size of time series and the hypothesized value of AR(1) parameter. To illustrate the findings of the paper, a financial data is analyzed. The practitioners should be careful about the hypothesized value of AR(1) parameter which represents dependency degree of the data. If the autoregressive parameters is very close to one and the break magnitude is high, any test is acceptable for moderate to large sample size. However, one might need very large sample size to have a good power and actual size of the test. Additionally, GH test becomes liberal test unlike EG test as the magnitude of structural break increases.

Keywords: Cointegration, Engle-Granger Cointegration Test, Gregory-Hansen Cointegration Test, Structural Break

Jel Classification: C15, C32, F65

Yapısal Kırılmalı İç Bağımlılığı Yüksek Zaman Serilerinde Eşbütünleşme Testlerinin Karşılaştırılması

Öz

Örneklem büyüklüğü, yapısal kırılmanın varlığı, potansiyel kırılmanın yeri ve büyüklüğü ve birim köke yakın prosese sahip olmak Eşbütünleşme testlerinin performanslarını etkileyebilir. Engle-Granger (EG) ve Johansen eşbütünleşme testleri, Gregory – Hansen (GH) eşbütünleşme testinden farklı olarak, olası kırılmaları dikkate almadığından hatalı sonuçlar verebilmektedir. Sözü geçen testlerin çıktıları bu özelliklerin yapısına çok duyarlı olduğundan, bu çalışmada uygun eşbütünleşme testinin seçilmesinin oldukça karmaşık olduğu tartışılmıştır. Eşbütünleşme testlerinin performansları belirtilen özellikler altında karşılaştırıldı. Bu çalışma, standart hata terimi tabanlı testlerin - Engle-Granger ve Gregory-Hansen- serilerin yüksek iç bağımlılığa (birim köke yakın süreçlere) sahip olduğunda nasıl uygulanabileceğini göstermektedir. Testlerin sonlu örneklem performansları değerlendirildiğinde, Monte Carlo deney sonuçları, her iki testin de kırılma noktası, kırılmanın büyüklüğü, serinin genişliği ve AR(1) parametresi değerleri için anlamlılık düzeyi ve güç değerleri açısından iyi sonuçlar verdiğini göstermiştir. Çalışmanın bulguları finansal veri ile de analiz edilmiştir. Araştırmacılar AR(1) modelin iç bağımlılığını gösteren parametrenin değerini test ederken dikkatli olmalıdırlar. Otoregresif modelin parametresinin bire çok yakın çıktığı ve yapısal kırılmanın büyüklüğünün yüksek olduğu durumda her iki test de büyük örneklem genişliği altında uygulanabilir. Ancak testlerin daha iyi güç değerlerine ve nominal anlamlılık düzeylerine sahip olması için çok büyük örneklemlere ihtiyaç vardır. Ek olarak yapısal kırılmanın büyüklüğü arttıkça Gregory – Hansen testi Engle Granger testine göre daha liberal davranışlar sergilemektedir.

Anahtar Kelimeler: Engle-Granger Eşbütünleşme Testi, Eşbütünleşme, Gregory-Hansen Eşbütünleşme Testi, Yapısal Kırılma

Suggested citation

Firuzan, E. & Çoban, B. (). Comparison of Cointegration Tests for Near Integrated Time Series Data with Structural Break. Alphanumeric Journal, 4(1), 35-44. http://dx.doi.org/10.17093/aj.2016.4.1.5000159943

bibtex

References

  • Akdi, Y. (2003), “Zaman serileri analizi (birim kökler ve kointegrasyon)”, Ankara. Bıçaklar Kitabevi
  • Bartley, W. A., Lee, J., Strazicich, M. C., (2001), “Testing the null of cointegration in the presence of a structural break”, Economics Letters 73 (3), 315–323.
  • Campos J., Ericsson N.R. and Hendry.D.F.(1996),”Cointegration test in the presence of structural breaks”, Journal of Econometrics, 70, 187–220.
  • Carrion-i-Silvestre, J. L., Sans`o, A., (2006). “Testing the null of cointegration with structural breaks.”, Oxford Bulletin of Economics and Statistics 68 (5), 623–646.
  • Enders, W. (1995). “Applied econometric time series (2nd ed.)”, Iowa State University. John Wiley & Sons.Inc.
  • Engle, R.F., Granger C. W. J. (1987). "Cointegration and Error Correction: Representation, Estimation and Testing", Econometrica 55,251-276
  • El-Shagi, M., Giesen S. (2013). "Testing for structural breaks at unknown time: A Steeplechase", Comput. Econ., 41,101-123
  • Gregory, A. W., Hansen B. E. (1996),” Residual-based tests for cointegration in models with regime shifts”, Journal of Econometrics, 70, 99-126
  • Granger, C.W.J. (1981), ”Some Properties of Time Series Data and Their Use in Econometric Model Specification”, Journal of Econometrics, 16, 121-130.
  • Granger C.W.J (1983): "Co-Integrated Variables and Error-Correcting Models," unpublished UCSD Discussion Paper 83-13.
  • Hamilton, J. D. (1994),” Time series analysis”, New Jersey: Princeton University Press.
  • Harris, D., Inder, B. (1994). “A test of the null of cointegration”, In: Hargreaves, C., ed. Nonstationary Time Series Analysis and Cointegration. Oxford: Oxford University Press, pp. 133–152.
  • Hao, K. (1996), “Testing for structural change in cointegrated regression models: some comparisons and generalizations”, Economet. Rev. 15:401–429.
  • Hendry, D.F., A.J. Neale (1991), “A Monte Carlo Study of the Effects of Structural Breaks on Tests for Unit Roots”, in P.Hackl and A. Westlund (eds.), Economic Structural Change, Springer Verlag, New York, 95-119
  • Hjalmarsson E., Österholm P.(2007). “A residual-based cointegration test for near root variables”, International Finance Discussion Papers with number 907.
  • Johansen S. (1995). “Likelihood-Based Inference in Cointegrated Vector Autoregressive Models”, Oxford. Oxford University Press
  • Kadılar, C. (2000), “Uygulamalı Çok Değişkenli Zaman Serileri Analizi”, Ankara: Bizim Büro Basımevi
  • Kwiatowski, D., Phillips, P. C. B., Schmidt, P. and Shin, Y. (1992) “Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root”, Journal of Econometrics, 54, 159–78.
  • Lee, J., Huang, C. J. and Shin, Y. (1997) “On stationarity tests in the presence of structural breaks”, Economics Letters, 55, 165–72.
  • Maddala, G. S. (1992). “Introduction to econometrics (2nd ed.)”, New York: Macmillan Publishing Company
  • Maddala G. S. & Kim I.M. (2003), ”Unit roots, cointegration and structural change (5th ed.)”, Cambridge: Cambridge University Press.
  • Perron, P.(1989). “The great crash, the oil-price shock, and the unit-root hypothesis. Econometrica”, Vol. 57, No. 6. (Nov., 1989), pp. 1361-1401
  • Perron, P. (1997), “Further Evidence on Breaking Trend Functions in Macroeconomic Variables”, Journal of Econometrics, 80 (2), pp.355-385.
  • Phillips, P. C. B. ( 1988b), “Regression theory for near-integrated time series”, Econometrica, 56, 1021-1043
  • Suzanna D.B., Granato J. (1999). 'Testing for cointegrating relationshipswith near-integrated data.' Political Analysis, 8(1): 99–117.
  • Yurdakul, F. (2000). Yapısal kırılmaların varlığı durumunda geliştirilen birim-kök testleri, Gazi Üniversitesi İ.İ.B.F. Dergisi, 2, 21-34
  • Zivot, E., & Andrews D.W.K. (1992). Further evidence on the great crash, the oil- price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics 10 (3), 251-270.

Volume 4, Issue 1, 2016

2016.04.01.ECON.01

alphanumeric journal

Volume 4, Issue 1, 2016

Pages 35-44

Received: Dec. 17, 2015

Accepted: Jan. 7, 2016

Published: June 30, 2016

Full Text [827.0 KB]

2016 Firuzan, E., Çoban, B.

This is an Open Access article, licensed under Creative Commons Attribution-NonCommercial 4.0 International License.

Creative Commons Attribution licence

scan QR code to access this article from your mobile device

Contact Us

Faculty of Transportation and Logistics, Istanbul University
Beyazit Campus 34452 Fatih/Istanbul/TURKEY

Bahadır Fatih Yıldırım, Ph.D.
editor@alphanumericjournal.com
+ 90 (212) 440 00 00 - 13219

alphanumeric journal

alphanumeric journal has been publishing as "International Peer-Reviewed Journal" every six months since 2013. alphanumeric serves as a vehicle for researchers and practitioners in the field of quantitative methods, and is enabling a process of sharing in all fields related to the operations research, statistics, econometrics and management informations systems in order to enhance the quality on a globe scale.