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Inference for the Lee-Carter Model With An AR(2) Process

Author

Listed:
  • Deyuan Li

    (Fudan University)

  • Chen Ling

    (Georgia State University)

  • Qing Liu

    (Jiangxi University of Finance and Economics)

  • Liang Peng

    (Georgia State University)

Abstract

Researchers in studying longevity risk often employ the Lee-Carter model with a unit root AR(1) process for unobserved mortality indexes. When one models the mortality index by a stationary AR(1) process, the widely used two-step inference in Lee and Carter (1992) is inconsistent. Some mortality datasets reject the unit root hypothesis. This paper develops consistent statistical inferences for a modified Lee-Carter model using an AR(2) process to model unobserved mortality indexes. It also provides a simulation study to examine their finite sample performance before applying them to the US mortality rates.

Suggested Citation

  • Deyuan Li & Chen Ling & Qing Liu & Liang Peng, 2022. "Inference for the Lee-Carter Model With An AR(2) Process," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 991-1019, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09898-y
    DOI: 10.1007/s11009-021-09898-y
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    References listed on IDEAS

    as
    1. Staudenmayer, John & Buonaccorsi, John P., 2005. "Measurement Error in Linear Autoregressive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 841-852, September.
    2. Qing Liu & Chen Ling & Liang Peng, 2019. "Statistical Inference for Lee-Carter Mortality Model and Corresponding Forecasts," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(3), pages 335-363, July.
    3. Kwok, Kai Yin & Chiu, Mei Choi & Wong, Hoi Ying, 2016. "Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 353-366.
    4. 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.
    5. Tat Wing Wong & Mei Choi Chiu & Hoi Ying Wong, 2017. "Managing Mortality Risk With Longevity Bonds When Mortality Rates Are Cointegrated," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 987-1023, September.
    6. John Staudenmayer & John P. Buonaccorsi, 2006. "Measurement Error in a Random Walk Model with Applications to Population Dynamics," Biometrics, The International Biometric Society, vol. 62(4), pages 1178-1189, December.
    7. Leng, Xuan & Peng, Liang, 2017. "Testing For A Unit Root In Lee–Carter Mortality Model," ASTIN Bulletin, Cambridge University Press, vol. 47(3), pages 715-735, September.
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