Finite-Sample Multivariate Tests for ARCH in Vector Autoregressive Models

In this paper we propose finite-sample multivariate tests for ARCH effects in the errors of vector autoregressive (VAR) models using Monte Carlo testing techniques and the bootstrap. The tests under consideration are combined equation-by-equation LM tests, multivariate LM tests and LM tests of constant error covariance matrix. We use a parametric bootstrap to circumvent the problem that the test statistics in VAR models are not free of nuisance parameters under the null hypothesis. The tests are evaluated in simulation experiments and the bootstrap tests are found to have excellent size and power properties. The LM tests of constant error covariance matrix outperform the combined LM tests and multivariate LM tests in terms of power.