Trend Adjustment Prior to Testing for the Cointegrating Rank of a Vector Autoregressive Process

Pentti Saikkonen and Helmut Lütkepohl

Journal of Time Series Analysis, 2000, vol. 21, issue 4, 435-456

Abstract: Testing the cointegrating rank of a vector autoregressive process that may have a deterministic linear trend is considered. Previous proposals for dealing with such a situation are either to allow for a deterministic trend term in computing a suitable test statistic or else to remove the linear trend first and then derive the test statistic from the trend‐adjusted data. In this study the latter approach is considered and a new method for trend removal is proposed that is based on estimating the trend parameters under the null hypothesis. Likelihood ratio and Lagrange multiplier type test statistics are derived on the basis of the trend‐adjusted data and their asymptotic distributions are considered under the null hypothesis and under local alternatives. A simulation comparison with other proposals is performed.

Date: 2000
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