Markov-Switching Multifractal Models for High-Frequency Trade Counts

This study extends the Markov-switching multifractal Poisson model for counts by incorporating zero inflation and adopting a generalized Poisson distribution. The zero-inflation component enables explicitly setting the probability of zeros, while the more general distribution provides control over the degree of conditional overdispersion and greater overall flexibility. Within this setting, we develop several analytical results to provide insight into the sources of count variation. The new models are applied to high-frequency trade count data for ten NYSE-listed stocks. The results suggest that the generalized Poisson distribution can account for part of the volatility generated by the intensity process in the basic model. This extension also performs best in-sample, with the lowest Bayesian information criterion for eight out of ten stocks. Out-of-sample, the zero-inflated specification appears to perform best overall, with the highest predictive likelihoods for six stocks. For point forecasting, other models are preferred, whereas for zero-event prediction it outperforms the alternatives for all but one stock. Taken together, the extensions can provide substantial improvements in the log likelihood, both in- and out-of-sample.