Adaptive models and heavy tails with an application to inflation forecasting

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, with the resulting model being observation-driven and being estimated using classical methods. In particular, we consider time variation in both the coefficients and the volatility, emphasizing how the two interact with each other. Meaningful restrictions are imposed on the model parameters in order to achieve local stationarity and bounded mean values. The model is applied to the analysis of inflation dynamics with the following results: allowing for heavy tails leads to significant improvements in terms of both the fit and forecasts, and the adoption of the Student-t distribution proves to be crucial for obtaining well-calibrated density forecasts. These results are obtained using the US CPI inflation rate and are confirmed by other inflation indicators, as well as for the CPI inflation of the other G7 countries.