A SEMI-MARKOV–HAWKES FRAMEWORK FOR MODELING SELF-ORGANIZING TRADING ACTIVITY

This study develops a combined Semi-Markov–Hawkes framework for describing the temporal organization of trading activity in a market. The proposed framework treats market behavior as a sequence of discrete events while distinguishing between two mechanisms that are often modeled independently: the duration of a market state and the endogenous clustering of subsequent events. The Semi-Markov component is used to represent state-dependent sojourn times without imposing the memoryless assumption, whereas the Hawkes component captures the tendency of previous transactions to increase the short-run probability of subsequent transactions. The framework also accommodates variations in trading intensity throughout the trading day and distinguishes among periods of low, moderate, and high market activity. An empirical illustration based on 30 days of observations of flour, meat, and chicken egg trading at a farmers' market in Nukus is used to demonstrate the proposed procedure. The resulting state dynamics indicate that low-activity conditions are persistent, moderate activity is comparatively transitional, and high-activity conditions are relatively short-lived. The estimated long-run state weights are 0.65, 0.30, and 0.05, respectively. These results demonstrate how the joint framework can be used to characterize market persistence, event clustering, and long-run equilibrium behavior within a unified probabilistic framework.