Filtering with heavy tails
An unobserved components model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on a conditional Student t-distribution, that is tractable and retains some of the desirable features of the linear Gaussian model. Letting the dynamics be driven by the score of the conditional distribution leads to a specification that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the ML estimator. The methods are illustrated with an application to rail travel in the UK. The .final part of the article shows how the model may be extended to include explanatory variables.
References listed on IDEAS
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- Alysha M De Livera & Rob J Hyndman, 2009. "Forecasting time series with complex seasonal patterns using exponential smoothing," Monash Econometrics and Business Statistics Working Papers 15/09, Monash University, Department of Econometrics and Business Statistics.
- Creal, Drew & Koopman, Siem Jan & Lucas, AndrÃ©, 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.
- Drew Creal & Siem Jan Koopman & AndrÃ© Lucas, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 552-563, October.
- Drew Creal & Siem Jan Koopman & André Lucas, 2010. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Tinbergen Institute Discussion Papers 10-032/2, Tinbergen Institute.
- Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
- Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
- Harvey, A. & Sucarrat, G., 2012. "EGARCH models with fat tails, skewness and leverage," Cambridge Working Papers in Economics 1236, Faculty of Economics, University of Cambridge.
- Gould, Phillip G. & Koehler, Anne B. & Ord, J. Keith & Snyder, Ralph D. & Hyndman, Rob J. & Vahid-Araghi, Farshid, 2008. "Forecasting time series with multiple seasonal patterns," European Journal of Operational Research, Elsevier, vol. 191(1), pages 207-222, November. Full references (including those not matched with items on IDEAS)
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