Dependence-based fuzzy clustering of functional time series

Time series clustering is essential for applications across fields like actuarial science, demography, and finance, yet methods for functional time series (collections of infinite-dimensional curves treated as random elements in a Hilbert space) remain underdeveloped. This work presents a novel clustering approach for functional time series by introducing a dissimilarity measure suited for functional data, which integrates with soft clustering techniques to assign gradual memberships to clusters. By extending quantile autocorrelation to the functional context, our method effectively groups time series with similar dependence structures, achieving high accuracy and computational efficiency in simulations. The approach's practical utility is demonstrated through case studies on high-frequency financial stock data and multi-country age-specific mortality improvements.