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Local power of likelihood‐based tests for cointegrating rank: Comparative analysis of full and partial systems

This note investigates local power properties of likelihood‐based cointegrating rank tests for partial and full vector autoregressive systems. The asymptotic distributions of partial likelihood‐based tests under local alternatives are derived, depending on various specifications of deterministic terms. A simulation study is then performed using both the full and partial systems. It is demonstrated that the rank tests based on the partial system, if a required parametric condition is fulfilled, can be more powerful than those based on the full system. This finding encourages testing cointegrating rank using a partial system as well as a full system, in such circumstances as the parametric condition could be satisfied.