Joint Long-Run Persistence and Cross-Age Dependence in Mortality: A Semiparametric Multivariate Long-Memory Framework

Recent studies have increasingly focused on persistence and long-memory behaviour in mortality data. However, existing research has examined persistence primarily from a marginal perspective, through separate univariate mortality processes, without jointly characterizing long-run persistence and dependence across mortality series. We investigate mortality persistence from a multivariate long-memory perspective by applying, for the first time, a semiparametric multivariate long-memory framework to mortality data. The framework is applied to Swedish mortality data after removing piecewise linear trends from age-group-specific time indices. The results reveal substantial long-run persistence and strong cross-age dependence within the multivariate mortality system, whereas little marginal persistence remains for most individual age groups after detrending. The multivariate long-run memory estimates range from 0.192 to 0.706. Moreover, the average pairwise long-run correlation is 0.655, compared with an average ordinary correlation of 0.526, indicating stronger dependence specifically at low frequencies. These findings suggest that mortality persistence is primarily a cross-age phenomenon rather than a marginal property of individual age-group dynamics. The estimated dependence structure also exhibits clear consecutive-age and age-cluster patterns. The long-run pairwise correlations among the three older age groups (50–64, 65–74, and 75–85) range from 0.927 to 0.952. Overall, the proposed framework provides a new perspective on mortality persistence by demonstrating the importance of analysing persistence jointly across age groups.