Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T00:53:42.913Z Has data issue: false hasContentIssue false
  • English
  • Français

DYNAMIC PRINCIPAL COMPONENT REGRESSION: APPLICATION TO AGE-SPECIFIC MORTALITY FORECASTING

Published online by Cambridge University Press:  20 June 2019

Han Lin Shang Open the ORCID record for Han Lin Shang [Opens in a new window]
Han Lin Shang*
Affiliation:
Research School of Finance, Actuarial Studies and Statistics, Level 4, Building 26CAustralian National University Kingsley Street, Acton, Canberra ACT 2601, Australia
*
E-Mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

In areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be treated as a discrete or continuous variable, a dimension reduction technique, such as principal component analysis (PCA), is often implemented. However, in the presence of moderate-to-strong temporal dependence, static PCA commonly used for analyzing independent and identically distributed data may not be adequate. As an alternative, we consider a dynamic principal component approach to model temporal dependence in a time series of curves. Inspired by Brillinger’s (1974, Time Series: Data Analysis and Theory. New York: Holt, Rinehart and Winston) theory of dynamic principal components, we introduce a dynamic PCA, which is based on eigen decomposition of estimated long-run covariance. Through a series of empirical applications, we demonstrate the potential improvement of 1-year-ahead point and interval forecast accuracies that the dynamic principal component regression entails when compared with the static counterpart.

Keywords

Dimension reductionfunctional time seriesKernel sandwich estimatorlong-run covariancemultivariate time series
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 3 , September 2019 , pp. 619 - 645
Copyright
© Astin Bulletin 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1974) A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59(3), 817–858.CrossRefGoogle Scholar
Booth, H., Hyndman, R.J., Tickle, L. and De Jong, P. (2006) Lee-Carter mortality forecasting: A multi-country comparison of variants and extensions. Demographic Research, 15, 289–310.CrossRefGoogle Scholar
Booth, H. and Tickle, L. (2008) Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science, 3(1–2), 3–43.CrossRefGoogle Scholar
Brillinger, D.R. (1974) Time Series: Data Analysis and Theory. New York: Holt, Rinehart and Winston.Google Scholar
De Boor, C. (2001), A Practical Guide to Splines, Vol. 27, Applied Mathematical Sciences, New York: Springer.Google Scholar
Gneiting, T. and Raftery, A.E. (2007) Strictly proper scoring rules, prediction and estimation. Journal of the American Statistical Association, 102(477), 359–378.CrossRefGoogle Scholar
Haberman, S. and Renshaw, A. (2012) Parametric mortality improvement rate modelling and projecting. Insurance: Mathematics and Economics, 50(3), 309–333.Google Scholar
Haberman, S. and Renshaw, A. (2013) Modelling and projecting mortality improvement rates using a cohort perspective. Insurance: Mathematics and Economics, 53(1), 150–168.Google Scholar
Horváth, L. and Kokoszka, P. (2012) Inference for Functional Data with Applications. New York: Springer.CrossRefGoogle Scholar
Human Mortality Database (2019) University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available at www.mortality.org or www.humanmortality.de (data downloaded on 12/June/2017).Google Scholar
Hyndman, R.J. and Khandakar, Y. (2008) Automatic time series forecasting: The forecast package for R. Journal of Statistical Software, 27(3), 1–22. http://dx.doi.org/10.18637/jss.v027.i03.CrossRefGoogle Scholar
Hyndman, R.J. and Shang, H.L. (2009) Forecasting functional time series (with discusssions). Journal of the Korean Statistical Society, 38(3), 199–221.CrossRefGoogle Scholar
Hyndman, R.J. and Shang, H.L. (2010) Rainbow plots, bagplots, and boxplots for functional data. Journal of Computational and Graphical Statistics, 19(1), 29–45.CrossRefGoogle Scholar
Hyndman, R.J. and Ullah, M.S. (2007) Robust forecasting of mortality and fertility rates: A functional data approach. Computational Statistics & Data Analysis, 51(10), 4942–4956.CrossRefGoogle Scholar
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. (1992) Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178.CrossRefGoogle Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Organization for Economic Co-Operation and Development [OECD] (2013) Pensions at a Glance 2013: OECD and G20 indicators, Technical report, OECD Publishing. Retrieved from http://dx.doi.org/10.1787/pension_glance-2013-en.Google Scholar
Renshaw, A.E. and Haberman, S. (2003) Lee-Carter mortality forecasting: A parallel generalized linear modelling approach for England and Wales mortality projections. Journal of the Royal Statistical Society: Series C, 52(1), 119–137.CrossRefGoogle Scholar
Rice, G. and Shang, H.L. (2017) A plug-in bandwidth selection procedure for long run covariance estimation with stationary functional time series. Journal of Time Series Analysis, 38(4), 591–609.CrossRefGoogle Scholar
Shang, H.L. (2012) Point and interval forecasts of age-specific life expectancies: A model averaging approach. Demographic Research, 27, 593–644.CrossRefGoogle Scholar
Shang, H.L. (2019) Visualizing rate of change: An application to age-specific fertility rates. Journal of the Royal Statistical Society: Series A, 182(1), 249–262.CrossRefGoogle Scholar
Shang, H.L., Booth, H. and Hyndman, R.J. (2011) Point and interval forecasts of mortality rates and life expectancy: A comparison of ten principal component methods. Demographic Research, 25, 173–214.CrossRefGoogle Scholar
Shang, H.L. and Haberman, S. (2017) Grouped multivariate and functional time series forecasting: An application to annuity pricing. Insurance: Mathematics and Economics, 75, 166–179.Google Scholar
Zhang, X. and Wang, J.-L. (2016) From sparse to dense functional data and beyond. The Annals of Statistics, 44(5), 2281–2321.CrossRefGoogle Scholar