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WAVELET-BASED FEATURE EXTRACTION FOR MORTALITY PROJECTION

Published online by Cambridge University Press:  25 June 2020

Donatien Hainaut Open the ORCID record for Donatien Hainaut [Opens in a new window]  and
Michel Denuit
Donatien Hainaut*
Affiliation:
Institute of Statistics, Biostatistis and Actuarial Science - ISBA Louvain Institute of Data Analysis and Modeling - LIDAM UCLouvain B-1348 Louvain-la-Neuve, Belgium E-Mails: donatien.hainaut@uclouvain.be; michel.denuit@uclouvain.be
Michel Denuit
Affiliation:
Institute of Statistics, Biostatistis and Actuarial Science - ISBA Louvain Institute of Data Analysis and Modeling - LIDAM UCLouvain B-1348 Louvain-la-Neuve, Belgium E-Mails: donatien.hainaut@uclouvain.be; michel.denuit@uclouvain.be
*
E-Mail: donatien.hainaut@uclouvain.be
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Abstract

Wavelet theory is known to be a powerful tool for compressing and processing time series or images. It consists in projecting a signal on an orthonormal basis of functions that are chosen in order to provide a sparse representation of the data. The first part of this article focuses on smoothing mortality curves by wavelets shrinkage. A chi-square test and a penalized likelihood approach are applied to determine the optimal degree of smoothing. The second part of this article is devoted to mortality forecasting. Wavelet coefficients exhibit clear trends for the Belgian population from 1965 to 2015, they are easy to forecast resulting in predicted future mortality rates. The wavelet-based approach is then compared with some popular actuarial models of Lee–Carter type estimated fitted to Belgian, UK, and US populations. The wavelet model outperforms all of them.

Keywords

Discrete wavelet transformmortality smoothingPoisson regressionregularizationLassoG22C01
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 675 - 707
Copyright
© 2020 by Astin Bulletin. All rights reserved

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