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Grouped multivariate and functional time series forecasting:An application to annuity pricing

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  • Shang, Han Lin
  • Haberman, Steven

Abstract

Age-specific mortality rates are often disaggregated by different attributes, such as sex, state, ethnic group and socioeconomic status. In making social policies and pricing annuity at national and subnational levels, it is important not only to forecast mortality accurately, but also to ensure that forecasts at the subnational level add up to the forecasts at the national level. This motivates recent developments in grouped functional time series methods (Shang and Hyndman, in press) to reconcile age-specific mortality forecasts. We extend these grouped functional time series forecasting methods to multivariate time series, and apply them to produce point forecasts of mortality rates at older ages, from which fixed-term annuities for different ages and maturities can be priced. Using the regional age-specific mortality rates in Japan obtained from the Japanese Mortality Database, we investigate the one-step-ahead to 15-step-ahead point-forecast accuracy between the independent and grouped forecasting methods. The grouped forecasting methods are shown not only to be useful for reconciling forecasts of age-specific mortality rates at national and subnational levels, but they are also shown to allow improved forecast accuracy. The improved forecast accuracy of mortality rates is of great interest to the insurance and pension industries for estimating annuity prices, in particular at the level of population subgroups, defined by key factors such as sex, region, and socioeconomic grouping.

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  • Shang, Han Lin & Haberman, Steven, 2017. "Grouped multivariate and functional time series forecasting:An application to annuity pricing," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 166-179.
  • Handle: RePEc:eee:insuma:v:75:y:2017:i:c:p:166-179
    DOI: 10.1016/j.insmatheco.2017.05.007
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    References listed on IDEAS

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    5. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
    6. Xiaoqian Wang & Yanfei Kang & Rob J Hyndman & Feng Li, 2020. "Distributed ARIMA Models for Ultra-long Time Series," Monash Econometrics and Business Statistics Working Papers 29/20, Monash University, Department of Econometrics and Business Statistics.
    7. Li, Han & Hyndman, Rob J., 2021. "Assessing mortality inequality in the U.S.: What can be said about the future?," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 152-162.
    8. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2020. "A more meaningful parameterization of the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 1-8.
    9. Melchior, Cristiane & Zanini, Roselaine Ruviaro & Guerra, Renata Rojas & Rockenbach, Dinei A., 2021. "Forecasting Brazilian mortality rates due to occupational accidents using autoregressive moving average approaches," International Journal of Forecasting, Elsevier, vol. 37(2), pages 825-837.
    10. Feng, Lingbing & Shi, Yanlin & Chang, Le, 2021. "Forecasting mortality with a hyperbolic spatial temporal VAR model," International Journal of Forecasting, Elsevier, vol. 37(1), pages 255-273.
    11. George Athanasopoulos & Puwasala Gamakumara & Anastasios Panagiotelis & Rob J Hyndman & Mohamed Affan, 2019. "Hierarchical Forecasting," Monash Econometrics and Business Statistics Working Papers 2/19, Monash University, Department of Econometrics and Business Statistics.
    12. Kaakaï, Sarah & Labit Hardy, Héloïse & Arnold, Séverine & El Karoui, Nicole, 2019. "How can a cause-of-death reduction be compensated for by the population heterogeneity? A dynamic approach," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 16-37.
    13. Li, Han & Li, Hong & Lu, Yang & Panagiotelis, Anastasios, 2019. "A forecast reconciliation approach to cause-of-death mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 122-133.
    14. Daniel Kosiorowski & Dominik Mielczarek & Jerzy. P. Rydlewski, 2017. "Forecasting of a Hierarchical Functional Time Series on Example of Macromodel for Day and Night Air Pollution in Silesia Region: A Critical Overview," Papers 1712.03797, arXiv.org.
    15. Hollyman, Ross & Petropoulos, Fotios & Tipping, Michael E., 2021. "Understanding forecast reconciliation," European Journal of Operational Research, Elsevier, vol. 294(1), pages 149-160.
    16. Daniel Kosiorowski & Dominik Mielczarek & Jerzy P. Rydlewski, 2017. "Aggregated moving functional median in robust prediction of hierarchical functional time series - an application to forecasting web portal users behaviors," Papers 1710.02669, arXiv.org, revised Jul 2018.

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