Integer-Valued Time Series Model via Copula-Based Bivariate Skellam Distribution

Time series analysis is crucial for modeling and forecasting diverse real-world phenomena. Traditional models typically assume continuous-valued data; however, many applications involve integer-valued series, often including negative integers. This paper introduces an approach that combines copula theory with the bivariate Skellam distribution to handle such integer-valued data effectively. Copulas are widely recognized for capturing complex dependencies among variables. By integrating copulas, our proposed method respects integer constraints while modeling positive, negative, and temporal dependencies accurately. Through simulation and an empirical study on a real-life example, we demonstrate that our class of models performs well. This approach has broad applicability in areas such as finance, epidemiology, and environmental science, where modeling series with integer values, both positive and negative, is essential.