Dynamic Score-Driven Models

Generalized autoregressive score (GAS) models offer a unified framework for time series modeling based on any underlying distribution with any time-varying parameters. The extensive GAS literature demonstrates that it is quite effective and natural to use the score of the conditional density function to drive the time-varying parameters. This doctoral thesis contributes to the framework from both theoretical and empirical perspectives. First, we identify several aspects in the GAS modeling which seem rather arbitrary or based purely on convenience: the choice of the parametrization of the underlying distribution, the link function, and the scaling function of the score. We investigate their impact on stochastic properties and the performance of dynamic models. We pay special attention to the GAS models based on the zero-inflated negative binomial distribution, for which we derive the consistency and asymptotic normality of the maximum likelihood estimator. Second, we propose three novel methodologies based on the GAS framework. (i) We propose a new general methodology for the treatment of arrivals clustering, which is based on the GAS model with the generalized gamma distribution. We find that ignoring the autocorrelation structure leads to significantly underestimated performance measures of queueing systems and consequently to suboptimal decisions. (ii) We propose a new approach to the high-frequency price modeling that directly takes the price clustering phenomenon into account. We base our GAS model on the mixture of several double Poisson distributions. In an empirical study of DJIA stocks, we find that higher instantaneous volatility leads to weaker price clustering at the ultra-high frequency, which is in sharp contrast with results at low frequencies. (iii) We propose a new distribution-free approach to the time-varying quantile modeling. We derive a Beta-t-IG model which resembles dynamics of the score-driven Beta-t-GARCH model by establishing a link between the time-varying quantiles and the time-varying dispersion.