Evidence for Persistence and Long Memory Features in Mortality Data

Abstract

It is important to understand the statistical features of mortality data if one is to accurately undertake mortality projection and forecasting when constructing life tables. The ability to accurately forecast mortality is a critical aspect for the study of demography, life insurance product design and pricing, pension planning and insurance based decision risk management. Though many stylised facts of mortality data have been discussed in the literature, we provide evidence for a novel statistical feature that is pervasive in mortality data at a national level that is as yet unexplored. In this regard we demonstrate in this work strong evidence for the existence of long memory features in mortality data. We argue that it is important to consider as incorporate of such features in models will improve the understanding of mortality and the accuracy of forecasts. To achieve this we first outline the way in which we choose to represent persistence of long memory from a estimator perspective. To achieve this, we make a natural link between a class of long memory feature and an attribute of stochastic processes based on fractional Brownian motion. This allows us to use well established estimators for the Hurst exponent to then robustly and accurately study the long memory features of mortality data. A series of synthetic studies are implemented to evaluate the performance of three different estimators under different data lengths, different long memory strengths, different missing value settings, different aggregation type and different quantization. All of which are common transformations used in studying national level mortality data. Then the dynamic of the long memory across genders, age groups, countries and time periods is further analysed using real data from a range of different countries to demonstrate overwhelming evidence for this statistical property of mortality data.