Is Arch Useful in High Frequency Foreign Exchange Applications?

Abstract

One of the many challenges posed by the study of high frequency financial market data is to develop models capable of explaining asset price behaviour at a range of frequencies. At the same time as presenting researchers with new opportunities, it also calls into question whether standard time series models are useful in high frequency applications. This paper addresses this issue from two perspectives. First, a Monte Carlo procedure is used to investigate whether the unconditional distribution of high frequency foreign exchange returns can be approximated by the unconditional distribution of returns simulated by a range of popular stochastic processes. Second, high frequency data is used to generate and appraise forecasts of daily variance. Forecasts are evaluated using statistical criteria as well as a profitability measure based on a trading game in a pseudo options market. The simulation exercise demonstrates that the autoregressive conditional heteroskedasticity (ARCH) family of models is unable to reproduce the unconditional distribution of foreign exchange returns at frequencies higher than 24 hours. This is largely a legacy of the heavy-tailed feature of intraday returns. However, results from the forecasting analysis extend those in Andersen and Bollerslev (1998) by showing that a range of standard volatility models can in fact produce accurate forecasts of realized daily variance. In other words, it is possible for ARCH models to predict variability in the conditional second moment of daily foreign exchange returns. This is attributed to the use of frequently sampled data in the construction of estimates of realized variance (against which forecasts are measured). In addition, the inclusion of the sum of squared intraday returns in the Generalized ARCH(1,1) model yields improvements in the modelling, and most notably forecasting, of realized daily variance. This appears to be an artifact of the noise inherent in using the daily squared return as an estimator of realized daily variance. This paper demonstrates that whilst standard econometric models do not capture the intraday foreign exchange return generating process, this should not immediately preclude these models from high frequency applications. Instead, the forecasting exercise demonstrates practical benefits are easily attainable from using high frequency data to develop and evaluate existing asset pricing models.