Adaptive Models and Heavy Tails

63 Pages Posted: 9 Jan 2016

See all articles by Ivan Petrella

Ivan Petrella

University of Warwick; University of Warwick - Finance Group; University of Warwick - Warwick Business School; Centre for Economic Policy Research (CEPR)

Davide Delle Monache

Bank of Italy

Multiple version iconThere are 2 versions of this paper

Date Written: January 8, 2016


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.

Keywords: Adaptive algorithms, student-t, inflation, score driven models, time-varying parameters

JEL Classification: C22, C51, C53, E31

Suggested Citation

Petrella, Ivan and Petrella, Ivan and Petrella, Ivan and Delle Monache, Davide, Adaptive Models and Heavy Tails (January 8, 2016). Bank of England Working Paper No. 577, Available at SSRN: or

Ivan Petrella (Contact Author)

University of Warwick - Warwick Business School ( email )

Coventry CV4 7AL
United Kingdom

University of Warwick - Finance Group ( email )

Gibbet Hill Rd
Coventry, CV4 7AL
Great Britain

University of Warwick ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

Davide Delle Monache

Bank of Italy ( email )

Via Nazionale 91
Rome, 00184

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