Discrete D-Vine Pair-Copula Estimation for Skellam Integer-Valued Time Series

Signed integer-valued time series arise naturally as differences between opposing counts, such as arrivals and departures, and require models that capture both their discrete nature and temporal dependence. We develop a Skellam regression framework that combines covariate effects with a flexible D-vine dependence structure. The approach accommodates positive and negative serial association and dependence extending beyond the immediately preceding observation. Two simulation examples evaluate estimation under first-order and higher-order dependence, demonstrating improved parameter recovery as sample size increases. An application to hourly net bicycle flows at a Montréal BIXI station illustrates the framework and compares alternative dependence specifications. Higher-order models provide modest improvements in fit, while a first-order model remains competitive. Residual diagnostics and simulation-based model checking identify some remaining discrepancies in the tails. An accompanying R implementation, supported by independent numerical verification, provides a reproducible framework for analyzing signed count time series.