DETECTING AND DIAGNOSTIC CHECKING MULTIVARIATE CONDITIONAL HETEROSCEDASTIC TIME SERIES MODELS

H. WONG^{1} AND W. K. LI^{2}

1Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon,

Hong Kong, China

2Department of Statistics & Actuarial Science, The University of Hong Kong, Hong Kong, China

(Received March 5, 1999; revised October 20, 2000)

Abstract. Two tests for multivariate conditional heteroscedastic models are proposed. One is based on the cross-correlations of standardized squared residuals and the other is a score (Lagrange multiplier) test. The cross-correlations test can be used to detect the presence of multivariate conditional heteroscedasticity whereas the other test can be used for diagnostic checking. Simulation studies on the size and power of the test statistics are reported. The application of the tests is illustrated by an example using the S & P 500 and Sydney All Ordinary Indexes.

Key words and phrases: ARCH models, squared residuals, cross-correlation tests, score test.