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MORTALITY FORECASTING WITH A SPATIALLY PENALIZED SMOOTHED VAR MODEL

Published online by Cambridge University Press:  04 November 2020

Le Chang Open the ORCID record for Le Chang [Opens in a new window]  and
Yanlin Shi
Le Chang*
Affiliation:
Research School of Finance, Actuarial Studies, and Statistics Australian National UniversityCanberra, ACT, Australia E-Mail: le.chang@anu.edu.au
Yanlin Shi
Affiliation:
Department of Actuarial Studies and Business Analytics Macquarie University Sydney, NSW, Australia E-Mail: yanlin.shi@mq.edu.au
*
E-Mail: le.chang@anu.edu.au
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Abstract

This paper investigates a high-dimensional vector-autoregressive (VAR) model in mortality modeling and forecasting. We propose an extension of the sparse VAR (SVAR) model fitted on the log-mortality improvements, which we name “spatially penalized smoothed VAR” (SSVAR). By adaptively penalizing the coefficients based on the distances between ages, SSVAR not only allows a flexible data-driven sparsity structure of the coefficient matrix but simultaneously ensures interpretable coefficients including cohort effects. Moreover, by incorporating the smoothness penalties, divergence in forecast mortality rates of neighboring ages is largely reduced, compared with the existing SVAR model. A novel estimation approach that uses the accelerated proximal gradient algorithm is proposed to solve SSVAR efficiently. Similarly, we propose estimating the precision matrix of the residuals using a spatially penalized graphical Lasso to further study the dependency structure of the residuals. Using the UK and France population data, we demonstrate that the SSVAR model consistently outperforms the famous Lee–Carter, Hyndman–Ullah, and two VAR-type models in forecasting accuracy. Finally, we discuss the extension of the SSVAR model to multi-population mortality forecasting with an illustrative example that demonstrates its superiority in forecasting over existing approaches.

Keywords

Mortality forecastinghigh-dimensional vector-autoregressive modelcohort effectaccelerated proximal gradientmulti-population modelingC18C32C52C53
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 161 - 189
Copyright
© 2020 by Astin Bulletin. All rights reserved

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Footnotes

*

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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