We introduce a nonlinear semi-parametric model that allows for the robust filtering of a common stochastic trend in a multivariate system of cointegrated time series. The observation-driven stochastic trend can be specified using flexible updating mechanisms. The model provides a general...

The equivalence of the Beveridge-Nelson decomposition and the trend-cycle decomposition is well established. In this paper we argue that this equivalence is almost immediate when a Gaussian score-driven location model is considered. We also provide a natural extension towards heavy-tailed...

We develop a score-driven time-varying parameter model where no particular parametric error distribution needs to be specified. The proposed method relies on a versatile spline-based density, which produces a score function that follows a natural cubic spline. This flexible approach nests the...

We characterize the dynamic properties of Generalized Autoregressive Score (GAS) processes by identifying regions of the parameter space that imply stationarity and ergodicity. We show how these regions are affected by the choice of parameterization and scaling, which are key features of GAS...

We introduce a new model for time-varying spatial dependence. The model extends the well-known static spatial lag model. All parameters can be estimated conveniently by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimator for 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....

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...

We study the performance of two analytical methods and one simulation method for computing in-sample confidence bounds for time-varying parameters. These in-sample bounds are designed to reflect parameter uncertainty in the associated filter. They are applicable to the complete class of...