Adaptive models and heavy tails

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 restrictions are imposed on the model parameters, so as to attain local stationarity and bounded mean values. In particular, we consider time variation in both coefficients and volatility, emphasizing how the two interact. The model is applied to the analysis of inflation dynamics. Allowing for heavy tails leads to significant improvements in terms of fit and forecast. The adoption of the Student-t distribution proves to be crucial in order to obtain well-calibrated density forecasts. These results are obtained using US CPI inflation rate and are confirmed for other indicators of inflation as well as the CPI inflation of the other G7 countries. Finally, we show how the proposed approach generalizes various adaptive algorithms used in the literature.