The evaluation of volatility models is gracefully complicated by the fact that, unlike other time series, even the realization is not observable. Two researchers would never disagree about what was yesterday’s stock price, but they can easily disagree about what was yesterday’s stock volatility. Because we don’t observe volatility directly, each of us uses own proxy of choice. There are many ways to skin this cat (more on volatility proxy here).
In a previous post Univariate volatility forecast evaluation we considered common ways in which we can evaluate how good is our volatility model, dealing with one time-series at a time. But how do we evaluate, or compare two models in a multivariate settings, with two covariance matrices?