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Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break
Article first published online: 26 NOV 2007
DOI: 10.1111/j.1467-9892.2007.00558.x
© 2007 The Authors
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How to Cite
Trenkler, C., Saikkonen, P. and Lütkepohl, H. (2008), Testing for the Cointegrating Rank of a VAR Process with Level Shift and Trend Break. Journal of Time Series Analysis, 29: 331–358. doi: 10.1111/j.1467-9892.2007.00558.x
Publication History
- Issue published online: 26 NOV 2007
- Article first published online: 26 NOV 2007
- First Version received December 2006
- Abstract
- Article
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- Cited By
Keywords:
- Cointegration;
- structural break;
- vector autoregressive process;
- error correction model
- C32.
Abstract. A test for the cointegrating rank of a vector autoregressive (VAR) process with a possible shift and broken linear trend is proposed. The break point is assumed to be known. Our test is not a likelihood ratio test but the deterministic terms including the broken trends are removed first by a generalized least squares procedure. Then, a likelihood ratio-type test is applied to the adjusted series. The asymptotic null distribution of the test is derived and it is shown by a Monte Carlo experiment that the test has better small-sample properties in many cases than a corresponding Gaussian likelihood ratio test for the cointegrating rank. Moreover, response surface techniques can be used to easily obtain p-values of the test for any possible break date.