Trends and random walks in mortality series

The notion that time series cannot be properly dealt with until their nature has been established is nowadays largely accepted among economists, less so among demographers. In this paper, based on theoretical considerations and empirical data, we prove that mortality evolves over time following a geometric random walk with drift. If this is true, other series too must follow a non-stationary path, for instance person-years and survivors in mortality tables, and survivors in actual populations. In the empirical part of the paper, we carry out 160 tests on age-specific log-mortality rates in France and England-Wales (at ages 0–79) over the years 1850–2016. The DS (difference stationary), not TS (trend stationary) nature of the series emerges clearly, probably with just one unit root.