Score-driven time-varying parameter models with splinebased densities

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 Gaussian density as a special case. It can also represent asymmetric and leptokurtic densities that produce outlier-robust updating functions for the time-varying parameter and are often appealing in empirical applications. As leading examples, we consider models where the time-varying parameters appear in the location or in the log-scale of the observations. The static parameter vector of the model can be estimated by means of maximum likelihood and we formally establish some of the asymptotic properties of such estimators. We illustrate the practical relevance of the proposed method in two empirical studies. We employ the location model to filter the mean of the U.S. monthly CPI inflation series and the scale model for volatility filtering of the full panel of daily stock returns from the S&P 500 index. The results show a competitive performance of the method compared to a set of competing models that are available in the existing literature.