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Risks 2017, 5(2), 21; doi:10.3390/risks5020021

Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, ACT 2601, Australia
Current address: Research School of Finance, Actuarial Studies and Statistics, Level 4, Building 26C, Australian National University, Kingsley Street, Canberra, ACT 2601, Australia.
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Author to whom correspondence should be addressed.
Academic Editor: Pavel Shevchenko
Received: 26 October 2016 / Revised: 15 March 2017 / Accepted: 21 March 2017 / Published: 25 March 2017
(This article belongs to the Special Issue Ageing Population Risks)
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Abstract

This study considers the forecasting of mortality rates in multiple populations. We propose a model that combines mortality forecasting and functional data analysis (FDA). Under the FDA framework, the mortality curve of each year is assumed to be a smooth function of age. As with most of the functional time series forecasting models, we rely on functional principal component analysis (FPCA) for dimension reduction and further choose a vector error correction model (VECM) to jointly forecast mortality rates in multiple populations. This model incorporates the merits of existing models in that it excludes some of the inherent randomness with the nonparametric smoothing from FDA, and also utilizes the correlation structures between the populations with the use of VECM in mortality models. A nonparametric bootstrap method is also introduced to construct interval forecasts. The usefulness of this model is demonstrated through a series of simulation studies and applications to the age-and sex-specific mortality rates in Switzerland and the Czech Republic. The point forecast errors of several forecasting methods are compared and interval scores are used to evaluate and compare the interval forecasts. Our model provides improved forecast accuracy in most cases. View Full-Text
Keywords: age-and sex-specific mortality rate; bootstrapping prediction interval; vector autoregressive model; vector error correction model; interval score age-and sex-specific mortality rate; bootstrapping prediction interval; vector autoregressive model; vector error correction model; interval score
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gao, Y.; Shang, H.L. Multivariate Functional Time Series Forecasting: Application to Age-Specific Mortality Rates. Risks 2017, 5, 21.

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