Futures Open Interest and Speculative Pressure Dynamics via Bayesian Models of Long‐Memory Count Processes

In this work, we develop time series regression models for long‐memory count processes based on the generalized linear Gegenbauer autoregressive moving average (GLGARMA) framework. We present a comprehensive Bayesian formulation that addresses both in‐sample and out‐of‐sample forecasting within a broad class of generalized count time series regression models. The GLGARMA framework supports various count distributions, including Poisson, negative binomial, generalized Poisson, and double Poisson distributions, offering the flexibility to capture key empirical characteristics such as underdispersion, equidispersion, and overdispersion in the data. We connect the counting process to a time series regression framework through a link function, which is associated with a stochastic linear predictor incorporating the family of long‐memory GARMA models. This linear predictor is central to the model's formulation, requiring careful specification of both the GLGARMA Bayesian likelihood and the resulting posterior distribution. To model the stochastic error terms driving the linear predictor, we explore two approaches: parameter‐driven and observation‐driven frameworks. For model estimation, we adopt a Bayesian approach under both frameworks, leveraging advanced sampling techniques, specifically the Riemann manifold Markov chain Monte Carlo (MCMC) methods implemented via R‐Stan. To demonstrate the practical utility of our models, we conduct an empirical study of open interest dynamics in US Treasury Bond Futures. Our Bayesian models are used to forecast speculative pressure, a crucial concept for understanding market behavior and agent actions. The analysis includes 136 distinct time series from the US Commodity Futures Trading Commission (CFTC), encompassing futures‐only and futures‐and‐options data across four US government‐issued fixed‐income securities. Our findings indicate that the proposed Bayesian GLGARMA models outperform existing state‐of‐the‐art models in forecasting open interest and speculative pressure. These improvements in forecast accuracy directly enhance portfolio performance, underscoring the practical value of our approach for bond futures portfolio construction. This work advances both the methodology for modeling long‐memory count processes and its application in financial econometrics, particularly in improving the forecasting of speculative pressure and its impact on investment strategies.