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Time series models with an EGB2 conditional distribution

Author

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  • Michele Caivano

    (Bank of Italy)

  • Andrew Harvey

    (University of Cambridge)

Abstract

A time series model in which the signal is buried in non-Gaussian noise may throw up observations that are outliers when judged by the Gaussian yardstick. We describe an observation-driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but that also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The model is fitted to US macroeconomic time series and compared with Gaussian and Student-t models. A theory is then developed for an EGARCH model based on the EGB2 distribution and the model is fitted to exchange rate data. Finally, dynamic location and scale models are combined and applied to data on the UK rate of inflation.

Suggested Citation

  • Michele Caivano & Andrew Harvey, 2014. "Time series models with an EGB2 conditional distribution," Temi di discussione (Economic working papers) 947, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_947_14
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    14. Michele Caivano & Andrew Harvey, 2014. "Time-series models with an EGB2 conditional distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 558-571, November.
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    Cited by:

    1. Harvey, Andrew & Palumbo, Dario, 2023. "Score-driven models for realized volatility," Journal of Econometrics, Elsevier, vol. 237(2).
    2. 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.
    3. Astrid Ayala & Szabolcs Blazsek & Adrian Licht, 2022. "Score-driven stochastic seasonality of the Russian rouble: an application case study for the period of 1999 to 2020," Empirical Economics, Springer, vol. 62(5), pages 2179-2203, May.
    4. Harvey, A. & Liao, Y., 2019. "Dynamic Tobit models," Cambridge Working Papers in Economics 1913, Faculty of Economics, University of Cambridge.
    5. Davide Delle Monache & Andrea De Polis & Ivan Petrella, 2024. "Modeling and Forecasting Macroeconomic Downside Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 1010-1025, July.
    6. Blasques, F. & van Brummelen, J. & Gorgi, P. & Koopman, S.J., 2024. "A robust Beveridge–Nelson decomposition using a score-driven approach with an application," Economics Letters, Elsevier, vol. 236(C).
    7. Blasques, Francisco & Nientker, Marc, 2023. "Stochastic properties of nonlinear locally-nonstationary filters," Journal of Econometrics, Elsevier, vol. 235(2), pages 2082-2095.
    8. Szabolcs Blazsek & Hector Hernández, 2018. "Analysis of electricity prices for Central American countries using dynamic conditional score models," Empirical Economics, Springer, vol. 55(4), pages 1807-1848, December.
    9. Saissi Hassani, Samir & Dionne, Georges, 2021. "The New International Regulation of Market Risk: Roles of VaR and CVaR in Model Validation," Working Papers 21-1, HEC Montreal, Canada Research Chair in Risk Management.
    10. Harvey, Andew & Liao, Yin, 2023. "Dynamic Tobit models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 72-83.
    11. Blasques, Francisco & van Brummelen, Janneke & Gorgi, Paolo & Koopman, Siem Jan, 2024. "Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions," Journal of Econometrics, Elsevier, vol. 238(1).
    12. M. Caivano & A. Harvey, 2013. "Two EGARCH models and one fat tail," Cambridge Working Papers in Economics 1326, Faculty of Economics, University of Cambridge.
    13. Michel Ferreira Cardia Haddad & Szabolcs Blazsek & Philip Arestis & Franz Fuerst & Hsia Hua Sheng, 2023. "The two-component Beta-t-QVAR-M-lev: a new forecasting model," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(4), pages 379-401, December.
    14. Sergio Contreras-Espinoza & Francisco Novoa-Muñoz & Szabolcs Blazsek & Pedro Vidal & Christian Caamaño-Carrillo, 2022. "COVID-19 Active Case Forecasts in Latin American Countries Using Score-Driven Models," Mathematics, MDPI, vol. 11(1), pages 1-17, December.
    15. Michele Caivano & Andrew Harvey, 2014. "Time-series models with an EGB2 conditional distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 558-571, November.
    16. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    17. Michele Caivano & Andrew Harvey & Alessandra Luati, 2016. "Robust time series models with trend and seasonal components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 99-120, March.
    18. Higbee, Joshua D. & McDonald, James B., 2024. "A comparison of the GB2 and skewed generalized log-t distributions with an application in finance," Journal of Econometrics, Elsevier, vol. 240(2).
    19. Harvey, A., 2021. "Score-driven time series models," Cambridge Working Papers in Economics 2133, Faculty of Economics, University of Cambridge.
    20. Jingyu Ji & Hang Lin, 2022. "Evaluating Regional Carbon Inequality and Its Dependence with Carbon Efficiency: Implications for Carbon Neutrality," Energies, MDPI, vol. 15(19), pages 1-35, September.
    21. Astrid Ayala & Szabolcs Blazsek, 2019. "Score-driven currency exchange rate seasonality as applied to the Guatemalan Quetzal/US Dollar," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 10(1), pages 65-92, March.

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    More about this item

    Keywords

    : beta distribution; EGARCH; fat tails; score; robustness; winsorizing;
    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
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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