Forecasting mortality with a hyperbolic spatial temporal VAR model

Accurate forecasts of mortality rates are essential to various types of demographic research like population projection, and to the pricing of insurance products such as pensions and annuities. Recent studies have considered a spatial–temporal vector autoregressive (STVAR) model for the mortality surface, where mortality rates of each age depend on the historical values for that age (temporality) and the neighboring cohorts ages (spatiality). This model has sound statistical properties including co-integrated dependent variables, the existence of closed-form solutions and a simple error structure. Despite its improved forecasting performance over the famous Lee–Carter (LC) model, the constraint that only the effects of the same and neighboring cohorts are significant can be too restrictive. In this study, we adopt the concept of hyperbolic memory to the spatial dimension and propose a hyperbolic STVAR (HSTVAR) model. Retaining all desirable features of the STVAR, our model uniformly beats the LC, the weighted functional demographic model, STVAR and sparse VAR counterparties for forecasting accuracy, when French and Spanish mortality data over 1950–2016 are considered. Simulation results also lead to robust conclusions. Long-term forecasting analyses up to 2050 comparing the four models are further performed. To illustrate the extensible feature of HSTVAR to a multi-population case, a two-population illustrative example using the same sample is further presented.