This paper proposes a novel and flexible framework to estimate autoregressive models with time-varying parameters. Our setup nests various adaptive algorithms that are commonly used in the macroeconometric literature, such as learning-expectations and forgetting-factor algorithms. These are...

In this paper we develop a general framework to analyze state space models with time-varying system matrices where time variation is driven by the score of the conditional likelihood. We derive a new filter that allows for the simultaneous estimation of the state vector and of the time-varying...

This paper introduces an adaptive algorithm for time-varying autoregressive models in presence of heavy tails. The evolution of the parameters is driven by the score of the conditional distribution. The resulting model is observation-driven and is estimated by classical methods. Meaningful...

This paper introduces an adaptive algorithm for time-varying autoregressive models in the presence of heavy tails. The evolution of the parameters is determined by the score of the conditional distribution. The resulting model is observation-driven and is estimated by classical methods....

We document a substantial increase in downside risk to US economic growth over the last 30 years. By modelling secular trends and cyclical changes of the predictive density of GDP growth, we find an accelerating decline in the skewness of the conditional distributions, with significant,...