Comparison Of Cointegration Tests For Near Integrated Time Series Data With Structural Break

1.526 466


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.

Full Text:




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.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.