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Dynamic mortality factor model with conditional heteroskedasticity

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  • Gao, Quansheng
  • Hu, Chengjun
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    Abstract

    In most methods for modeling mortality rates, the idiosyncratic shocks are assumed to be homoskedastic. This study investigates the conditional heteroskedasticity of mortality in terms of statistical time series. We start from testing the conditional heteroskedasticity of the period effect in the naïve Lee-Carter model for some mortality data. Then we introduce the Generalized Dynamic Factor method and the multivariate BEKK GARCH model to describe mortality dynamics and the conditional heteroskedasticity of mortality. After specifying the number of static factors and dynamic factors by several variants of information criterion, we compare our model with other two models, namely, the Lee-Carter model and the state space model. Based on several error-based measures of performance, our results indicate that if the number of static factors and dynamic factors is properly determined, the method proposed dominates other methods. Finally, we use our method combined with Kalman filter to forecast the mortality rates of Iceland and period life expectancies of Denmark, Finland, Italy and Netherlands.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4X66S18-1/2/f277e50775c2f7f8b22c736fc87c70b6
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 3 (December)
    Pages: 410-423

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    Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:410-423

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Lee-Carter model Generalized dynamic factor model Multivariate generalized autoregressive conditionally heteroskedastic model Mortality forecasting Kalman filter;

    References

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    1. Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2006. "Dynamic Factor GARCH: Multivariate Volatility Forecast for a Large Number of Series," LEM Papers Series 2006/25, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    2. James G. MacKinnon, 1995. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Working Papers 918, Queen's University, Department of Economics.
    3. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
    4. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
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    7. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
    8. Bauer Daniel & Börger Matthias & Ruß Jochen & Zwiesler Hans-Joachim, 2008. "The Volatility of Mortality," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(1), pages 1-29, September.
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    10. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    11. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2008. "A robust criterion for determining the number of static factors in approximate factor models," Working Paper Series 0903, European Central Bank.
    12. Renshaw, A. E. & Haberman, S., 2003. "On the forecasting of mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 379-401, July.
    13. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
    14. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    15. Taufiq Choudhry & Hao Wu, 2008. "Forecasting ability of GARCH vs Kalman filter method: evidence from daily UK time-varying beta," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 670-689.
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    Cited by:
    1. Hatzopoulos, P. & Haberman, S., 2011. "A dynamic parameterization modeling for the age-period-cohort mortality," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 155-174, September.

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