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**Dynamic mortality factor model with conditional heteroskedasticity.**
*(English)*
Zbl 1231.91187

Summary: 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.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

62M07 | Non-Markovian processes: hypothesis testing |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

### Keywords:

Lee-Carter model; generalized dynamic factor model; multivariate generalized autoregressive conditionally heteroskedastic model; mortality forecasting; Kalman filter### Software:

LifeMetrics
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\textit{Q. Gao} and \textit{C. Hu}, Insur. Math. Econ. 45, No. 3, 410--423 (2009; Zbl 1231.91187)

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### References:

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