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.