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Information-Theoretic Time-Varying Density Modeling

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  • Bram van Os

    (Erasmus University Rotterdam)

Abstract

We present a comprehensive framework for constructing dynamic density models by combining optimization with concepts from information theory. Specifically, we propose to recursively update a time-varying conditional density by maximizing the log-likelihood contribution of the latest observation subject to a Kullback-Leibler divergence (KLD) regularization centered at the one-step ahead predicted density. The resulting Relative Entropy Adaptive Density (READY) update has attractive optimality properties, is reparametrization invariant and can be viewed as an intuitive regularized estimator of the pseudo-true density. Popular existing models, such as the ARMA(1,1) and GARCH(1,1), can be retrieved as special cases. Furthermore, we show that standard score-driven models with inverse Fisher scaling can be derived as convenient local approximations of the READY update. Empirical usefulness is illustrated by the modeling of employment growth and asset volatility.

Suggested Citation

  • Bram van Os, 2023. "Information-Theoretic Time-Varying Density Modeling," Tinbergen Institute Discussion Papers 23-037/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20230037
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    References listed on IDEAS

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    1. F. Blasques & S. J. Koopman & A. Lucas, 2015. "Information-theoretic optimality of observation-driven time series models for continuous responses," Biometrika, Biometrika Trust, vol. 102(2), pages 325-343.
    2. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    3. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    4. Panos Toulis & Thibaut Horel & Edoardo M. Airoldi, 2021. "The proximal Robbins–Monro method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 188-212, February.
    5. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    6. Harvey, Andrew & Oryshchenko, Vitaliy, 2012. "Kernel density estimation for time series data," International Journal of Forecasting, Elsevier, vol. 28(1), pages 3-14.
    7. Blasques, Francisco & van Brummelen, Janneke & Koopman, Siem Jan & Lucas, André, 2022. "Maximum likelihood estimation for score-driven models," Journal of Econometrics, Elsevier, vol. 227(2), pages 325-346.
    8. Anne Opschoor & Pawel Janus & André Lucas & Dick Van Dijk, 2018. "New HEAVY Models for Fat-Tailed Realized Covariances and Returns," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 643-657, October.
    9. Lucas, André & Zhang, Xin, 2016. "Score-driven exponentially weighted moving averages and Value-at-Risk forecasting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 293-302.
    10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    11. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64, Elsevier.
    12. Paolo Gorgi, 2020. "Beta–negative binomial auto‐regressions for modelling integer‐valued time series with extreme observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1325-1347, December.
    13. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    14. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
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    Cited by:

    1. Eric A. Beutner & Yicong Lin & Andre Lucas, 2023. "Consistency, distributional convergence, and optimality of score-driven filters," Tinbergen Institute Discussion Papers 23-051/III, Tinbergen Institute.

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