Nonlinearity in High-Frequency Financial Data and Hierarchical Models

This paper studies nonlinear behavior of high-frequency financial data and employs nonlinear hierarchical models for analyzing such data. We illustrate the analysis by modeling the transaction-bytransaction data of IBM stock on the New York Stock Exchange for a period of 3 months. The variables considered include time durations between trades and price changes. For a short time span of 5 trading days, a simple threshold model is found adequate for modeling time durations between trades after adjusting for the diurnal pattern of the data. When price change and time duration between price changes are considered jointly, we use a hierarchical model that consists of 6 simple conditional models to handle the dynamic structure within a trading day and the variation between trading days for the whole sample. The model shows that dynamic structure exists in the high-frequency data, but there are some special days on which the behavior of the stock seems different from the others. We use Markov chain Monte Carlo methods to estimate the hierarchical model.