Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Harris, David; Leybourne, Stephen J.; Taylor, A.M. Robert (2016)
Publisher: Elsevier
Journal: Journal of Econometrics
Languages: English
Types: Article
Subjects: Applied Mathematics, History and Philosophy of Science, Economics and Econometrics
In this paper we consider the problem of testing for the co-integration rank of a vector autoregressive process in the case where a trend break may potentially be present in the data. It is known that un-modelled trend breaks can result in tests which are incorrectly sized under the null hypothesis and inconsistent under the alternative hypothesis. Extant procedures in this literature have attempted to solve this inference problem but require the practitioner to either assume that the trend break date is known or to assume that any trend break cannot occur under the co-integration rank null hypothesis being tested. These procedures also assume the autoregressive lag length is known to the practitioner. All of these assumptions would seem unreasonable in practice. Moreover in each of these strands of the literature there is also a presumption in calculating the tests that a trend break is known to have happened. This can lead to a substantial loss in finite sample power in the case where a trend break does not in fact occur. Using information criteria based methods to select both the autoregressive lag order and to choose between the trend break and no trend break models, using a consistent estimate of the break fraction in the context of the former, we develop a number of procedures which deliver asymptotically correctly sized and consistent tests of the co-integration rank regardless of whether a trend break is present in the data or not. By selecting the no break model when no trend break is present, these procedures also avoid the potentially large power losses associated with the extant procedures in such cases.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Andrews, D.W.K. (1993). Tests for parameter instability and structural change with unknown change point. Econometrica 61, 821|56 (Corrigendum, 71, 395|7).
    • Bai, J. (1994). Least squares estimation of a shift in a linear process. Journal of Time Series Analysis 15, 453|472.
    • Cavaliere, G., A. Rahbek and A.M.R. Taylor (2010). Co-integration rank testing under conditional heteroskedasticity. Econometric Theory 26, 1719{1760.
    • Cheung, Y-W. and K.S. Lai (1993) Finite-sample sizes of Johansen's likelihood ratio tests for cointegration. Oxford Bulletin of Economics and Statistics 55, 313{328.
    • Harris, D., D.I. Harvey, S.J. Leybourne and A.M.R. Taylor (2009). Testing for a unit root in the presence of a possible break in trend. Econometric Theory 25, 1545|1588.
    • Harris, D., S.J. Leybourne and A.M.R. Taylor (2015). Supplement to `Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point'.
    • Inoue, A. (1999). Tests of cointegrating rank with a trend-break, Journal of Econometrics 90, 215{ 237.
    • Johansen S. (1992). Determination of cointegration rank in the presence of a linear trend. Oxford Bulletin of Economics and Statistics 54, 383|397.
    • Johansen, S. (2002). A sample correction of the test for cointegrating rank in the vector autoregressive model. Econometrica 70, 1929{1961.
    • Johansen, S. (1995). Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.
    • Johansen, S., R. Mosconi and B. Nielsen (2000). Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal 3, 216|49.
    • Kim, D. and P. Perron (2009). Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses. Journal of Econometrics 148, 1{13.
    • Kim J-Y. (2012). Model selection in the presence of nonstationarity. Journal of Econometrics 169, 247-257.
    • Lutkepohl, H. and P. Saikkonen (1999). Order selection in testing for the cointegrating rank of a VAR process, In: Cointegration, Causality, and Forecasting. A Festschrift in Honour of Clive W.J. Granger, R.F. Engle and H. White (eds.), Oxford: Oxford University Press, 168{199
    • Lutkepohl, H., P. Saikkonen and C. Trenkler (2004). Testing for the cointegrating rank of a VAR process with a structural shift at unknown time. Econometrica72, 647|62.
    • Perron, P. (1989). The Great Crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 1361|401.
    • Perron, P. (1997). Further evidence of breaking trend functions in macroeconomic variables. Journal of Econometrics 80, 355|385.
    • Perron, P. and J.Y. Campbell (1993). A note on Johansen's cointegration procedure when trends are present. Empirical Economics 18, 777{789.
    • Perron, P. and Z. Qu (2007). A modi ed information criterion for cointegration tests based on a VAR approximation. Econometric Theory 23, 638{685.
    • Perron, P. and X. Zhu (2005). Structural breaks with deterministic and stochastic trends. Journal of Econometrics 129, 65|119.
    • Qu, Z. and P. Perron (2007). Estimating and testing structural changes in multivariate regressions. Econometrica 75, 459|502.
    • Saikkonen, P. and H. Lutkepohl (2000). Testing for the cointegration rank of a VAR process with structural shifts. Journal of Business & Economic Statistics 18, 451|64.
    • Schwarz, G. (1978). Estimating the dimension of a model, Annals of Statistics 6, 461{464.
    • Stock, J.H. and M.W. Watson (1996). Evidence on structural instability in macroeconomic time series relations. Journal of Business and Economic Statistics 14, 11|30.
    • Stock, J.H. and M.W. Watson (1999). A comparison of linear and nonlinear univariate models for forecasting macroeconomic time series. In R.F. Engle and H. White (eds.), Cointegration, Causality and Forecasting: A Festschrift in Honour of Clive W.J. Granger, pp. 1{44. Oxford University Press.
    • Stock, J. and M.W. Watson (2005). Implications of Dynamic Factor Analysis for VAR Models, NBER Working paper 11467.
  • No related research data.
  • No similar publications.

Share - Bookmark

Funded by projects

  • RCUK | The Analysis of Non-statio...

Cite this article