A multivariate time series approach to projected life tables. (English) Zbl 1224.91069

This paper investigates the use of multivariate time series techniques for forecasting age-specific death rates. The authors extend the Lee-Carter model to the dynamic factor models and the common trends approach. It is pointed out the equivalence between the common trends representation and the cointegration approach. The dynamic relationships among the series of age-specific death rates are estimated with the help of the Johansen maximum likelihood methodology. An empirical illustration performed on Belgian mortality statistics is presented. The Johansen cointegration methodology is used to generate forecasts for the death rates by using a vector-error correction model.


91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Lee, Modelling and forecasting U.S. mortality, Journal of the American Statistical Association 87 pp 659– (1992)
[2] Lee, The LeeâCarter method for forecasting mortality, with various extensions and applications, North American Actuarial Journal 4 pp 80– (2000) · Zbl 1083.62535
[3] Girosi F King G Understanding the LeeâCarter mortality forecasting method 2007
[4] Hari, Estimating the term structure of mortality, Insurance: Mathematics and Economics 42 pp 492– (2008)
[5] Lazar D On forecasting mortality using LeeâCarter method
[6] Booth, Applying LeeâCarter under conditions of variable mortality decline, Population Studies 56 pp 325– (2002)
[7] Girosi, Demographic Forecasting (2006)
[8] Brouhns, A Poisson log-bilinear approach to the construction of projected lifetables, Insurance: Mathematics and Economics 31 pp 373– (2002) · Zbl 1074.62524
[9] Renshaw, LeeâCarter mortality forecasting with age specific enhancement, Insurance: Mathematics and Economics 33 pp 255– (2003) · Zbl 1103.91371
[10] Renshaw, LeeâCarter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections, Applied Statistics 52 pp 119– (2003) · Zbl 1111.62359
[11] Renshaw AE Haberman S LeeâCarter mortality forecasting incorporating bivariate time series for England and Wales mortality projections 2005
[12] Tuljapurkar, A universal pattern of mortality decline in the G7 countries, Nature 405 pp 789– (2000)
[13] Chang Y Miller JI Park JY Extracting a common stochastic trend: theories with some applications 2005
[14] Johansen, Likelihood-based Inference in Cointegrated Vector Autoregressive Models (1995) · Zbl 0928.62069
[15] Engle, Cointegration and error correction: representation, estimation, and testing, Econometrica 55 pp 251– (1987) · Zbl 0613.62140
[16] Johansen, Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control 12 pp 231– (1988) · Zbl 0647.62102
[17] Johansen, Estimation and hypothesis of cointegration vectors in Gaussian vector autoregressive models, Econometrica 59 pp 1551– (1991) · Zbl 0755.62087
[18] Hubrich, A review of systems cointegration tests, Econometrica Reviews 20 pp 247– (2001) · Zbl 1044.62120
[19] Juselius, The Cointegrated VAR Model: Methodology and Applications (2006) · Zbl 1258.91006
[20] Harris, Applied Time Series Modeling and Forecasting (2003)
[21] Trenkler, A new set of critical values for systems cointegration tests with a prior adjustment for deterministic terms, Economics Bulletin 11 pp 1– (2003)
[22] Reinsel, Vector autoregressive models with unit roots and reduced rank structure: estimation, likelihood ratio test, and forecasting, Journal of Time Series Analysis 13 pp 353– (1992) · Zbl 0770.62079
[23] LÃ{\(\tfrac14\)}tkepohl, Introduction to Multiple Time Series Analysis (1991)
[24] Hendry, Explaining cointegration analysis, part 2, The Energy Journal 22 pp 75– (2001)
[25] Lee, Evaluating the performance of the LeeâCarter approach to modeling and forecasting mortality, Demography 38 pp 537– (2001)
[26] Chamberlain, Arbitrage, factor structure and meanâvariance analysis in large asset markets, Econometrica 51 pp 1305– (2003)
[27] Bai, Inferential theory for factor models of large dimensions, Econometrica 71 pp 135– (2003) · Zbl 1136.62354
[28] Stock, Macroeconomic forecasting using diffusion indexes, Journal of Business and Economic Statistics 20 pp 147– (2002)
[29] Nielsen, Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach, Journal of Econometrics 141 pp 574– (2007) · Zbl 1418.62344
[30] Hyndman, Robust forecasting of mortality and fertility rates: a functional data approach, Computational Statistics and Data Analysis 51 pp 4942– (2007) · Zbl 1162.62434
[31] Booth, LeeâCarter mortality forecasting: a multi-country comparison of variants and extensions, Demographic Research 15 pp 289– (2006)
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