We study the performance of alternative methods for calculating in-sample confidence and out of-sample forecast bands for time-varying parameters. The in-sample bands reflect parameter uncertainty only. The out-of-sample bands reflect both parameter uncertainty and innovation uncertainty. The...

We propose a new Markov switching model with time varying probabilities for the transitions. The novelty of our model is that the transition probabilities evolve over time by means of an observation driven model. The innovation of the time varying probability is generated by the score of the...

We study the strong consistency and asymptotic normality of the maximum likelihood estimator for a class of time series models driven by the score function of the predictive likelihood. This class of nonlinear dynamic models includes both new and existing observation driven time series models....

A new model for time-varying spatial dependencies is introduced. It forms an extension to the popular spatial lag model and can be estimated conveniently by maximum likelihood. The spatial dependence parameter is assumed to follow a generalized autoregressive score (GAS) process. The theoretical...

We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The...