Evaluating Volatility and Correlation Forecasts

Abstract

This chapter considers the problem of evaluation and comparison of univariate and multivariate volatility forecasts, with explicit attention paid to the fact that in such applications the object of interest is unobserv- able, even ex post. Thus the evaluation and comparison of volatility forecasts must rely on direct or indirect methods of overcoming this difficulty. Direct methods use a “volatility proxy”, i.e. some observable vari- able that is related to the latent variable of interest. We will assume the existence of an unbiased volatility proxy, such as daily squared returns for the daily conditional variance of returns. Indirect methods of over- coming the latent nature of the variable of interest include comparing forecasts via mean-variance portfolio decisions or comparisons based on portfolio “tracking error”.