Score-Driven Models: Methodology and Theory

Score-driven models belong to a wider class of observation-driven time series models that are used intensively in empirical studies in economics and finance. A defining feature of the score-driven model is its mechanism of updating time-varying parameters by means of the score function of the predictive likelihood function. The class of score-driven models contains many other well-known observation-driven models as special cases, and many new models have been developed based on the score-driven principle. Score-driven models provide a general way of parameter updating, or filtering, in which all relevant features of the observation density function are considered. In models with fat-tailed observation densities, the score-driven updates are robust to large observations in time series. This kind of robustness is a convenient feature of score-driven models and makes them suitable for applications in finance and economics, where noisy data sets are regularly encountered. Parameter estimation for score-driven models is straightforward when the method of maximum likelihood is used. In many cases, theoretical results are available under rather general conditions.