This paper propose to incorporate the family of Gegenbauer Autoregressive Moving Average (GARMA) models and a special sub family called the Autoregressive Fractionally Integrated Moving Average (ARFIMA) models into the mean functions of count distributions, including Poisson, Negative Binomial (NB), Generalized Poisson (GP) and Double Poisson (DP). These distributions display equi-, over- and under-dispersion features and the additional long memory structure enhances modelling flexibility. Furthermore, we define the error terms of the GARMA family under two different approaches, the parameter-driven and observation-driven approaches. To estimate these models, we adopt a Bayesian approach implemented using R package Rstan. Then Deviance Information Criterion is evaluated to select some best-fitting models to undertake forecasting of these different classes of long memory count time series. The models are applied to analyse 136 individual U.S. Commodity Futures Trading Commission (CFTC) time series of counts which are each related to trade volume for futures-only and futures-and-options crossed classified with four fixed income securities provided by the U.S. federal government: Treasury notes (T-notes) at 2, 5 and 10 years and Treasury bonds (T-bonds) at marturities of 20 or 30 year terms. These represent some of the most active futures contracts traded in financial markets. The analysis developed provides the first detailed study of this kind undertaken by market participant type according to the categories of reportables and non-reportables and sub-categories of positions of their trading behaviours categorised by the buy and sell sides of long-call, short-put and spread being the difference between long-call and short-put. Furthermore, we study the disaggregated reportables data according to the CFTC four categories of traders, namely, dealers, asset managers, leveraged funds and other reportables. The studies performed demonstrate particular long-memory structures are consistently observed in these highly liquid and important financial instruments and in particular demonstrate systematic forecastable patterns in trading behaviour and liquidity by market participant type, which is as yet not reported or identified in financial literature. Such findings are then directly used as forecasting tools to study further relationships between price discovery and price volatility dynamics.
Yan, H., Chan, J. S. K., & Peters, G. W. (2017). Long Memory Models for Financial Time Series of Counts and Evidence of Systematic Market Participant Trading Behaviour Patterns in Futures on US Treasuries. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2962341