Finite Sample Optimality of Score-Driven Volatility Models: Some Monte Carlo Evidence

Abstract

Optimality properties are studied in finite samples for time-varying volatility models driven by the score of the predictive likelihood function. Available optimality results for this class of models suffer from two drawbacks. First, they are only asymptotically valid when evaluated at the pseudo-true parameter. Second, they only provide an optimality result ‘on average’ and do not provide conditions under which such optimality prevails. Using finite sample Monte Carlo experiments, it is shown that score-driven volatility models have optimality properties when they matter most. Score-driven models perform best when the data are fat-tailed and robustness is important. Moreover, they perform better when filtered volatilities differ most across alternative models, such as in periods of financial distress. These simulation results are supplemented by an empirical application based on U.S. stock returns.