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Adaptive models and heavy tails

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  • Petrella, Ivan

    () (Bank of England)

  • Delle Monache, Davide

    () (Banca d'Italia)

Abstract

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.

Suggested Citation

  • Petrella, Ivan & Delle Monache, Davide, 2016. "Adaptive models and heavy tails," Bank of England working papers 577, Bank of England.
  • Handle: RePEc:boe:boeewp:0577
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    Cited by:

    1. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    2. F Blasques & P Gorgi & S Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models," Papers 1610.02863, arXiv.org.
    3. Kapetanios, George & Marcellino, Massimiliano & Venditti, Fabrizio, 2016. "Large Time-Varying Parameter VARs: A Non-Parametric Approach," CEPR Discussion Papers 11560, C.E.P.R. Discussion Papers.
    4. Mauro Bernardi & Leopoldo Catania, 2016. "Comparison of Value-at-Risk models using the MCS approach," Computational Statistics, Springer, vol. 31(2), pages 579-608, June.
    5. repec:eee:eecrev:v:100:y:2017:i:c:p:293-317 is not listed on IDEAS
    6. Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2016. "Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models," Tinbergen Institute Discussion Papers 16-082/III, Tinbergen Institute.
    7. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Optimal Formulations for Nonlinear Autoregressive Processes," Tinbergen Institute Discussion Papers 14-103/III, Tinbergen Institute.
    8. Delle Monache, Davide & Petrella, Ivan & Venditti, Fabrizio, 2016. "Adaptive state space models with applications to the business cycle and financial stress," CEPR Discussion Papers 11599, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    Adaptive algorithms; student-t; inflation; score driven models; time-varying parameters;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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