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Time-varying coefficient models with ARMA-GARCH structures for longitudinal data analysis

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  • Haiyan Zhao
  • Fred Huffer
  • Xu-Feng Niu

Abstract

Time-varying coefficient models with autoregressive and moving-average-generalized autoregressive conditional heteroscedasticity structure are proposed for examining the time-varying effects of risk factors in longitudinal studies. Compared with existing models in the literature, the proposed models give explicit patterns for the time-varying coefficients. Maximum likelihood and marginal likelihood (based on a Laplace approximation) are used to estimate the parameters in the proposed models. Simulation studies are conducted to evaluate the performance of these two estimation methods, which is measured in terms of the Kullback-Leibler divergence and the root mean square error. The marginal likelihood approach leads to the more accurate parameter estimates, although it is more computationally intensive. The proposed models are applied to the Framingham Heart Study to investigate the time-varying effects of covariates on coronary heart disease incidence. The Bayesian information criterion is used for specifying the time series structures of the coefficients of the risk factors.

Suggested Citation

  • Haiyan Zhao & Fred Huffer & Xu-Feng Niu, 2015. "Time-varying coefficient models with ARMA-GARCH structures for longitudinal data analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 309-326, February.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:2:p:309-326
    DOI: 10.1080/02664763.2014.949638
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    References listed on IDEAS

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    1. Menelaos Karanasos, "undated". "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. David E. Rapach & Jack K. Strauss, 2008. "Structural breaks and GARCH models of exchange rate volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 65-90.
    4. Skaug, Hans J. & Fournier, David A., 2006. "Automatic approximation of the marginal likelihood in non-Gaussian hierarchical models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 699-709, November.
    5. Menelaos Karanasos, 2001. "Prediction in ARMA Models with GARCH in Mean Effects," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 555-576, September.
    6. 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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