Evaluating Volatility and Correlation Forecasts

This chapter considers the problems of evaluation and comparison of volatility forecasts, both univariate (variance) and multivariate (covariance matrix and/or correlation). We pay explicit attention to the fact that the object of interest in these applications is unobservable, even ex post, and so the evaluation and comparison of volatility forecasts often rely on the use of a “volatility proxy”, i.e. an observable variable that is related to the latent variable of interest. We focus on methods that are robust to the presence of measurement error in the volatility proxy, and to the conditional distribution of returns.