A Discrete Time Series Model for High Frequency Financial Data

In this paper a flexible model for correlation in high frequency data is proposed, which maintains the data’s discrete nature and captures features such as asymmetry and excess zeros. The model uses an a theoretical approach based on that of an ARIMA model. This model works with price changes and does not restrict the size of the price change. The model employs a combination of different distributions to model price changes. An unbounded discrete distribution was used to model the size of the change combined with a multinomial to determine the direction of the change and provide an excess number of zeros. A binominal thinning operator was used to model the correlation. The model was estimated for correlation in high frequency share price and exchange rate data. Results are presented for seven data sets. Two have an excess number of zeros and four exhibit asymmetry. An ARCH equation can be readily incorporated into the model, but the results here demonstrate that an excess number of zeros can be misinterpreted as ARCH when a continuous model is fitted.