ABSTRACT
As a result of this increasing awareness of the potential for means, variances, and covariances of asset returns to change over time, an everincreasing and powerful array of econometric tools have been introduced that allow quantitative analysts to make inferences and predictions on the current and future means, variances, and covariances of asset returns. The first step in this direction was taken in the literature on time-varying volatility, a phenomenon commonly termed conditional heteroskedasticity (CH), a term borrowed from the statistical literature to indicate that the variances and covariances of the series of interest may change as a function of current information on the state of the economy or the financial markets. Since the seminal work by Robert Engle (see, e.g., Engle et al., 1987), we know that for most financial return series and frequencies, simple time-series models of the autoregressive moving average (ARMA) type may be used to successfully model and forecast time variation in financial volatility. In practice, this means that asset returns are much riskier at some times than others. As early as in the late 1980s, the literature on models of conditional variances has been extended to encompass multivariate applications in which ARMA models are adopted to describe and predict the dynamics of conditional covariances and hence correlations (see Bollerslev et al., 1988, for an early attempt).
