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Adaptive models and heavy tails
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Adaptive models and heavy tails

Author

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  • Davide Delle Monache

    (Bank of Italy)

  • Ivan Petrella

    (Bank of England)

Abstract

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.

Suggested Citation

  • Davide Delle Monache & Ivan Petrella, 2016. "Adaptive models and heavy tails," Temi di discussione (Economic working papers) 1052, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_1052_16
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    Cited by:

    1. Barbara Rossi, 2019. "Forecasting in the Presence of Instabilities: How Do We Know Whether Models Predict Well and How to Improve Them," Working Papers 1162, Barcelona School of Economics.
    2. 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.
    3. 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.
    4. Dave, Chetan & Malik, Samreen, 2017. "A tale of fat tails," European Economic Review, Elsevier, vol. 100(C), pages 293-317.
    5. Henrik Jensen & Ivan Petrella & Søren Hove Ravn & Emiliano Santoro, 2020. "Leverage and Deepening Business-Cycle Skewness," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(1), pages 245-281, January.
    6. F Blasques & P Gorgi & S J Koopman & O Wintenberger, 2016. "Feasible Invertibility Conditions for Maximum Likelihood Estimation for Observation-Driven Models ," Working Papers hal-01377971, HAL.
    7. George Kapetanios & Massimiliano Marcellino & Fabrizio Venditti, 2019. "Large time‐varying parameter VARs: A nonparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(7), pages 1027-1049, November.
    8. Petrella, Ivan & Venditti, Fabrizio & Delle Monache, Davide, 2016. "Adaptive state space models with applications to the business cycle and financial stress," CEPR Discussion Papers 11599, C.E.P.R. Discussion Papers.
    9. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Optimal Formulations for Nonlinear Autoregressive Processes," Tinbergen Institute Discussion Papers 14-103/III, Tinbergen Institute.
    10. 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.
    11. 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.

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    More about this item

    Keywords

    adaptive algorithms; inflation; score driven models; student-t; time-varying parameters.;
    All these keywords.

    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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