Groupe d’études et de recherche en analyse des décisions

G-2002-45

A Test for Multivariate Autoregressive Conditional Heteroskedasticity Effects in Vector Time Series Models

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We propose a test to detect multivariate ARCH effects in the residuals from a multivariate regression model. The absence of ARCH effects implies that the spectral density of the squared and cross-residuals is the uniform density on the interval [-,]. Alternatively, when ARCH effects are present, the spectral density is generally not uniform. Our test is based on a comparison between a kernel-based spectral density estimator of the squared and cross-residuals and the uniform density via a norm. A new application of Hosking's (1980) test is a special case using the uniform truncated kernel. However, using a different weighting, more powerful procedures are typically obtained. The procedure of Robinson (1991) is considered for the choice of the smoothing parameter of the spectral density estimator. This makes the proposed test fully operational in practice. Finite sample performance of the tests are investigated and an application with financial data is considered.

, 30 pages