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**A comparison of the Lee-Carter model and AR-ARCH model for forecasting mortality rates.**
*(English)*
Zbl 1235.91089

Summary: With the decline in the mortality level of populations, national social security systems and insurance companies of most developed countries are reconsidering their mortality tables taking into account the longevity risk. The Lee and Carter model is the first discrete-time stochastic model to consider the increased life expectancy trends in mortality rates and is still broadly used today. In this paper, we propose an alternative to the Lee-Carter model: an AR(1)-ARCH(1) model. More specifically, we compare the performance of these two models with respect to forecasting age-specific mortality in Italy. We fit the two models, with Gaussian and t-student innovations, for the matrix of Italian death rates from 1960 to 2003. We compare the forecast ability of the two approaches in out-of-sample analysis for the period 2004–2006 and find that the AR(1)-ARCH(1) model with t-student innovations provides the best fit among the models studied in this paper.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

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

### Keywords:

mortality rates; Lee-Carter model; autoregression-autoregressive conditional heteroskedasticity model; AR(1)-ARCH(1) model### Software:

LifeMetrics
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\textit{R. Giacometti} et al., Insur. Math. Econ. 50, No. 1, 85--93 (2012; Zbl 1235.91089)

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