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Data graduation based on statistical time series methods

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  • Guerrero, Victor M.
  • Juárez, Rodrigo
  • Poncela, Pilar

Abstract

Whittaker's method is one of the most frequently employed techniques to graduate mortality tables. In order for the method to work and produce reasonable results, some subjective input is required from the graduator. In this paper we show that Whittaker' s solution to the graduation problem can be approached from a statistical time series model-based perspective that reduces the subjectivity in its application. It also serves to interpret the graduation problem as a classical estimation problem. In fact, on the basis of some suitable assumptions, we are able to show thatthe Best Linear Unbiased Estimator of the true mortality rates has the form of Whittaker's solution. We also provide some complementary analytical tools aimed at helping the graduator to employ the method in practice and interpret its results from a statistical standpoint. A numerical illustration is shown in detail to exemplify the application of our proposal.

Suggested Citation

  • Guerrero, Victor M. & Juárez, Rodrigo & Poncela, Pilar, 1997. "Data graduation based on statistical time series methods," DES - Working Papers. Statistics and Econometrics. WS 6213, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6213
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    References listed on IDEAS

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    1. Verrall, R. J., 1993. "A state space formulation of Whittaker graduation, with extensions," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 7-14, September.
    2. Taylor, Greg, 1992. "A Bayesian interpretation of Whittaker--Henderson graduation," Insurance: Mathematics and Economics, Elsevier, vol. 11(1), pages 7-16, April.
    3. Guerrero, Victor M., 1993. "Combining historical and preliminary information to obtain timely time series data," International Journal of Forecasting, Elsevier, vol. 9(4), pages 477-485, December.
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    Cited by:

    1. Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    2. Guerrero, Victor M., 2007. "Time series smoothing by penalized least squares," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1225-1234, July.
    3. Cortez, Willy Walter & Islas-Camargo, Alejandro, 2009. "How Correlated are Mexico’s Salaries and Us Output? an Inquiry on Some Us Border Cities," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(08), pages 35-62, primer se.

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    Keywords

    Best linear unbiased estimation;

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