Integrated Volatility and UHF-GARCH Models: A Comparison Using High Frequency Financial Data

Abstract

A very promising literature has been recently devoted to the modeling of ultra-high-frequency (UHF) data. The main problem encountered to measure volatility dynamics of high-frequency intra-daily data lies in the irregularity at which observations arrive. Engle and Russell (1998) have proposed a new class of point processes with dependent arrival rates: autoregressive conditional duration (ACD) point processes. Engle (2000) has generalized this approach and developed a Ultra-High-Frequency GARCH model. At the same time, Andersen and Bollerslev (1998) and Bollerslev and Wright (2001) have studied the volatility of UHF financial data by introducing the concept of integrated volatility. This integrated volatility is measured by the squared value of intra-daily returns. Our first aim in this paper is to develop an empirical application of ACD GARCH models in forecasting future volatilities. Then we propose another contribution in comparing the performances of ACD GARCH models with the integrated volatility. Therefore we propose a procedure to take into account the calendar effect or the time of day effect. We introduce an adjusted duration to calculate volatilities before comparing volatility forecasts. We show that the models induced by the two approaches lead to poor performances. Nevertheless, our results show that the integrated volatility method tends to outperform UHF-GARCH models.