Multivariate modelling of the autoregressive random variance process

Abstract

The autoregressive random variance (ARV) model proposed by Taylor (Financial returns modelled by the product of two stochastic processes, a study of daily sugar prices 1961-79. In Time Series Analysis: Theory and Practice 1 (ed. O. D. Anderson). Amsterdam: North-Holland, 1982, pp. 203-26) is useful in modelling stochastic changes in the variance structure of a time series. In this paper we focus on a general multivariate ARV model. A traditional EM algorithm is derived as the estimation method. The proposed EM approach is simple to program, computationally efficient and numerically well behaved. The asymptotic variance-covariance matrix can be easily computed as a by-product using a well-known asymptotic result for extremum estimators. A result that is of interest in itself is that the dimension of the augmented state space form used in computing the variance-covariance matrix can be shown to be greatly reduced, resulting in greater computational efficiency. The multivariate ARV model considered here is useful in studying the lead-lag (causality) relationship of the variance structure across different time series. As an example, the leading effect of Thailand on Malaysia in terms of variance changes in the stock indices is demonstrated.