Multivariate tests for autocorrelation in the stable and unstable VAR models

This study investigates the size and power properties of three multivariate tests for autocorrelation, namely portmanteau test, Lagrange multiplier (LM) test and Rao F-test, in the stable and unstable vector autoregressive (VAR) models, with and without autoregressive conditional heteroscedasticity (ARCH) using Monte Carlo experiments. Many combinations of parameters are used in the simulations to cover a wide range of situations in order to make the results more representative. The results of conducted simulations show that all three tests perform relatively well in stable VAR models without ARCH. In unstable VAR models the portmanteau test exhibits serious size distortions. LM and Rao tests perform well in unstable VAR models without ARCH. These results are true, irrespective of sample size or order of autocorrelation. Another clear result that the simulations show is that none of the tests have the correct size when ARCH is present irrespective of VAR models being stable or unstable and regardless of the sample size or order of autocorrelation. The portmanteau test appears to have slightly better power properties than the LM test in almost all scenarios.