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Age-Specific Death Rates Smoothed by the Gompertz–Makeham Function and Their Application in Projections by Lee–Carter Model

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Time Series Analysis and Forecasting

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

The aim of this paper is to use stochastic modelling approach (Lee–Carter model) for the case of age-specific death rates for the Czech population. We use an annual empirical data from the Czech Statistical Office (CZSO) database for the period from 1920 to 2012. We compare two approaches for modelling between each other, one is based on the empirical time series of age-specific death rates and the other one is based on smoothed time series by the Gompertz–Makeham function, which is currently the most frequently used tool for smoothing of mortality curve at higher ages. (Our review also includes a description of other advanced models which are commonly used.) Based on the results of mentioned approaches we compare two issues of time series forecasting—variability and stability. Sometimes stable development of time series can be the correct issue which ensure significant and realistic prediction, sometimes not. In the case of mortality it is necessary to consider both unexpected or stochastic changes and long-term stable deterministic trend. Between them we have to find a mutual compromise.

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Acknowledgements

This paper was supported by the Czech Science Foundation project No. P402/12/G097 DYME—Dynamic Models in Economics.

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Authors and Affiliations

  1. Department of Statistics and Probability, University of Economics Prague, Faculty of Informatics and Statistics, W. Churchill sq. 4, 130 67, Prague, Czech Republic

    Ondřej Šimpach & Petra Dotlačilová

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  1. Ondřej Šimpach
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  2. Petra Dotlačilová
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Correspondence to Ondřej Šimpach .

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Editors and Affiliations

  1. CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

  2. CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

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Šimpach, O., Dotlačilová, P. (2016). Age-Specific Death Rates Smoothed by the Gompertz–Makeham Function and Their Application in Projections by Lee–Carter Model. In: Rojas, I., Pomares, H. (eds) Time Series Analysis and Forecasting. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28725-6_18

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