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. 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. Moreover, we show how the proposed approach generalizes the various adaptive algorithms used in the literature. 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's-t distribution proves to be crucial in order to obtain well-calibrated density forecasts. These results are obtained using the US CPI inflation rate and are confirmed by other inflation indicators as well as the CPI of the other G7 countries.
Pubblicato nel 2017 in: International Journal of Forecasting, v. 33, 2, pp. 482-501.