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Double Generalized Threshold Models with constraint on the dispersion by the mean

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  • Wu, K.Y.K.
  • Li, W.K.

Abstract

Generalized Threshold Model (GTM) is a non-linear time series model which generalizes the Threshold Autoregressive Model (TAR) to implement the idea of the Generalized Linear Model under the threshold time series framework. However, the dispersion parameter is usually assumed as constant in the context of Generalized Linear Model which does not hold in general. In this paper, the GTM is extended to a Double Generalized Threshold Model (DGTM) where the dispersion parameter, defined as the expected deviance of the individual response about its mean, varies throughout the entire sample. The variation of the dispersion parameter can be predicted by another threshold type generalized linear model, which is interlinked with the threshold model for the mean and can be estimated simultaneously.

Suggested Citation

  • Wu, K.Y.K. & Li, W.K., 2015. "Double Generalized Threshold Models with constraint on the dispersion by the mean," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 59-73.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:59-73
    DOI: 10.1016/j.csda.2014.08.003
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    References listed on IDEAS

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    1. Noelle I. Samia & Kung-Sik Chan & Nils Chr. Stenseth, 2007. "A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan," Biometrika, Biometrika Trust, vol. 94(1), pages 101-118.
    2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    3. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    4. Chao Wang & Heng Liu & Jian-Feng Yao & Richard A. Davis & Wai Keung Li, 2014. "Self-Excited Threshold Poisson Autoregression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 777-787, June.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Noelle I. Samia & Kung-Sik Chan, 2011. "Maximum likelihood estimation of a generalized threshold stochastic regression model," Biometrika, Biometrika Trust, vol. 98(2), pages 433-448.
    7. Li, Dong & Ling, Shiqing & Li, Wai Keung, 2013. "Asymptotic Theory On The Least Squares Estimation Of Threshold Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 29(3), pages 482-516, June.
    8. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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