Combined Lagrange multiplier test for ARCH in vector autoregressive models

A combined Lagrange multiplier (LM) test for autoregressive conditional heteroskedastic (ARCH) errors in vector autoregressive (VAR) models is proposed by replacing an exact Monte Carlo (MC) test by a bootstrap MC test when the model includes lags. The test circumvents the problem of high dimensionality in multivariate tests for ARCH in VAR models. It only requires computing univariate statistics. A computational advantage is therefore that the number of parameters to be estimated is independent of the dimension of the VAR process. The bootstrap MC test is shown to be asymptotically valid. Monte Carlo simulations show that the test has good finite-sample properties. The test is robust against a non-normal error distribution. Two financial applications of multivariate LM tests for ARCH to credit default swap (CDS) prices and Euribor interest rates are presented. The results indicate that the errors are skewed and heavy-tailed, and that there are significant ARCH effects.