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An autoregressive model based on the generalized hyperbolic distribution

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  • Henri Karttunen

Abstract

We define a nonlinear autoregressive time series model based on the generalized hyperbolic distribution in an attempt to model time series with non‐Gaussian features such as skewness and heavy tails. We show that the resulting process has a simple condition for stationarity and it is also ergodic. An empirical example with a forecasting experiment is presented to illustrate the features of the proposed model.

Suggested Citation

  • Henri Karttunen, 2020. "An autoregressive model based on the generalized hyperbolic distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 787-816, September.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:3:p:787-816
    DOI: 10.1111/sjos.12427
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    References listed on IDEAS

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    1. Leena Kalliovirta & Mika Meitz & Pentti Saikkonen, 2015. "A Gaussian Mixture Autoregressive Model for Univariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 247-266, March.
    2. Patton, Andrew J. & Timmermann, Allan, 2007. "Properties of optimal forecasts under asymmetric loss and nonlinearity," Journal of Econometrics, Elsevier, vol. 140(2), pages 884-918, October.
    3. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    4. Leena Kalliovirta, 2012. "Misspecification tests based on quantile residuals," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 358-393, June.
    5. Mika Meitz & Daniel Preve & Pentti Saikkonen, 2023. "A mixture autoregressive model based on Student’s t–distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(2), pages 499-515, January.
    6. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    7. Yu, Jun, 1999. "Forecasting Volatility in the New Zealand Stock Market," Working Papers 175, Department of Economics, The University of Auckland.
    8. Dorsey, Robert E & Mayer, Walter J, 1995. "Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability, and Other Irregular Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 53-66, January.
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