Long Memory Process in Asset Returns with Multivariate GARCH innovations

The main purpose of this paper is to consider the multivariate GARCH (MGARCH) framework to model the volatility of a multivariate process exhibiting long term dependence in stock returns. More precisely, the long term dependence is examined in the …first conditional moment of US stock returns through multivariate ARFIMA process and the time-varying feature of volatility is explained by MGARCH models. An empirical application to the returns series is carried out to illustrate the usefulness of our approach. The main results confi…rm the presence of long memory property in the conditional mean of all stock returns.