This paper presents several forecasting methods to model and forecast subnational age distribution of death counts. The age distribution of death counts resembles strong similarities with probability density functions, which are nonnegative and have a constrained integral and thus live in a constrained nonlinear space. To address the nonlinear nature of objects, we implement a compositional data analytic approach known as centered log-ratio (clr) transformation to transformmultiple densities into unconstrained functions. However, the clr transformation cannot handle the presence of zero values. This motivates us to consider a new cumulative distribution function (CDF) transformation with additional monotonicity. Using the Japanese subnational life-table death counts obtained from the [4], we evaluate the forecast accuracy of the transformations and forecasting methods. The improved forecast accuracy of life-table death counts is of great interest to demographers for estimating regional age-specific survival probabilities and life expectancy and actuaries for the pricing of annuities and setting of reserves.

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Forecasting Age Distribution of Deaths at Subnational Level

  • Han Lin Shang

摘要

This paper presents several forecasting methods to model and forecast subnational age distribution of death counts. The age distribution of death counts resembles strong similarities with probability density functions, which are nonnegative and have a constrained integral and thus live in a constrained nonlinear space. To address the nonlinear nature of objects, we implement a compositional data analytic approach known as centered log-ratio (clr) transformation to transformmultiple densities into unconstrained functions. However, the clr transformation cannot handle the presence of zero values. This motivates us to consider a new cumulative distribution function (CDF) transformation with additional monotonicity. Using the Japanese subnational life-table death counts obtained from the [4], we evaluate the forecast accuracy of the transformations and forecasting methods. The improved forecast accuracy of life-table death counts is of great interest to demographers for estimating regional age-specific survival probabilities and life expectancy and actuaries for the pricing of annuities and setting of reserves.