Residual Autocorrelation Testing for Vector Error Correction Models

In applied time series analysis, checking for autocorrelation in a fitted model is a routine diagnostic tool. Therefore it is useful to know the asymptotic and small sample properties of the standard tests for the case when some of the variables are cointegrated. The properties of residual autocorrelations of vector error correction models (VECMs) and tests for residual autocorrelation are derived. In particular, the asymptotic distributions of Lagrange multiplier (LM) and portmanteau tests are given. Monte Carlo simulations show that the LM tests have advantages if autocorrelation of small order is tested whereas portmanteau tests are preferable for higher order residual autocorrelation. Their critical values have to be adjusted for the cointegration rank of the system, however.