Prediction intervals for future mortality rates

Abstract

The vector t 1 m  of N age-specific mortality rates in year t+1 is modeled to be dependent on the vector t m in the present year t and l-1 other vectors before year t via a conditional distribution which is derived from an N(l+1)-dimensional power-normal distribution. The marginal distribution of the mortality rate at age x is computed from the conditional distribution. The prediction interval with end points given by the 100(α/2) and 100(1-α/2) percentage points of the marginal distribution is used to predict the mortality rate at age x in year t+1. The similar idea is used to find a prediction interval for the mortality rate at age x in year t+d where d >1. The United States mortality data from 1933 to 2000 are used to estimate the N(l+1)-dimensional power-normal distribution. The prediction intervals based on the distributions when N=19, l=1 and 2 are found to have good ability of covering the observed future mortality rates in the years from 2001 to 2010. The length of the prediction interval may be shortened by choosing small values of N and using more recent historical data. Mathematics Subject Classification: 62M10, 62P05

Prediction of mortality rates using a model with stochastic parameters

“…, where E y , H is an orthogonal matrix that consists of the eigenvectors of the variance-covariance matrix of y, which will then specify a lag (l-1) multivariate time series model for the vector of c n time-dependent correlated observations. With the assumption that the multivariate time series is stationary, we may consider that the vector , , Constructing a lag-0 model for a vector of three age-specific total death rates in [6] and [8], the nominally 95% prediction intervals for the total death rates of the age group 60-64 were obtained, which are summarized in TABLE 1. In this table, d…”

“…In this section, we will incorporate time-varying stochastic parameters into the methodology by Pooi et al [6]. In [6], [8] and [9], the training data consisted of mortality rates from the years 1933 till 2000 (68 years) while the testing data consisted of mortality rates from the years 2001 till 2010 (10 years). Intuitively, among the data in the full training dataset, the earlier death rates may be less informative than the recent death rates in reflecting the "future" mortality range in the testing dataset.…”

“…In [6], Pooi et al applied a time series model based on multivariate power-normal (MPN) distribution to obtain prediction intervals for future age-specific mortality rates of the United States (US). The US mortality data from the years 1933 till 2000 was fitted with a MPN distribution, which then is used to obtain the prediction intervals for future death rates of the years 2001 till 2010.…”

“…Subsequently, this methodology was also applied in cases where the data used was augmented to include female death rates, death rates of Canada and UK [8] as well as applied on incomplete US mortality training dataset that contains missing values [9]. In general, the resulting prediction intervals in [6], [8] and [9] were found to have good ability in covering the observed future death rates. Although the prediction interval lengths may become longer for long-run prediction in [9], the prediction intervals in [8] performed well as they tend to have shorter interval lengths.…”

“…The layout of this paper is as follows. In the next section, the multivariate time series given in [5] is briefly introduced and some results on prediction of deaths rates given in [6] and [8] are highlighted. The subsequent section provides the prediction results obtained using the model with stochastic parameters.…”