A comparison of the accuracy of short term foreign exchange forecasting methods

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Abstract

The hypothesis that foreign exchange rate behaviour is non-linear has been examined by several authors; others have proposed a linear framework. Here, evidence for a non-linear generating process is evaluated by an analysis of the comparative accuracy of short term forecasts of FX rates. Forecasts were generated by a linear AR-GARCH model and four non-linear methods, including three nearest neighbour methods and locally weighted regression. Five data frequencies were used: daily, four-hourly, two-hourly, hourly and half-hourly. Using root mean square error as a measure, significantly greater accuracy than a no-change forecast was achieved for two-hourly and higher frequency data sets. Using a test by Peseran and Timmerman, significant predictive directional accuracy was found for four-hourly and higher frequency data sets. These results were supported by simulated trading based on forecast direction. No evidence was found that the FX rate behaviour is better represented by a non-linear generating process than by a linear model.

Introduction

The hypothesis that the behaviour of foreign exchange rates is, to some extent, non-linear has been examined by several authors. The evidence for a non-linear data generating process for foreign exchange rates is examined further here by the evaluation of the comparative accuracy of short term forecasts from methods based on linear and non-linear hypotheses. The linear forecasting method uses an ARMA-GARCH time series model. Two non-linear forecasting methods are used: one is a local non-parametric method using nearest neighbours; the second is a locally weighted regression. Forecast accuracy is considered from two viewpoints: point accuracy and directional accuracy of the change in exchange rate (equivalent to the sign of the period to period return). A random walk model for foreign exchange rates is used as a naı̈ve benchmark. The data used are of five frequencies: daily, four-hourly, two-hourly, hourly and half-hourly, although only the intra-day data are discussed in detail.

A range of conventional error measures is used to provide evidence about comparative accuracy of the forecasting methods. The sensitivity of the ranking of the forecasting methods to the choice of accuracy measure used is discussed in detail. For each accuracy measure, a formal significance test is used to assess the economic value of the forecasts. Tests of the significance of the directional accuracy of the forecasts are also carried out.

The structure of the paper is as follows. Details of the data are given in Section 2. Section 3 describes the forecasting methods used and their backgrounds, and details of the relevant parameters are given for each data set. Section 4 contains a description of the error measures used and formal tests for differences in accuracy are identified. An analysis of the accuracy measures by data set and forecasting method follows. Conclusions are given in Section 5.

Section snippets

Description of data

The data sets are foreign exchange rates for the US$ against the UK£, the German Mark and the Japanese Yen. These will be referred to respectively by the following codes: USDGBP, USDDEM and USDJPY. Table 1 gives full details of the dates and size of the data sets. The intra-day data from 1997 forms the basis for this analysis, the daily data and the 1986 hourly data will be mentioned solely for comparative purposes. The availability of half-hourly data permitted the observation of lower

Forecasting methods

The GARCH model, linear in mean and non-linear in variance, has been used by many authors. This model has been used to capture the heteroskedasticity of daily foreign exchange rates by, for example, Baillie and Bollerslev (1989), Milhoj (1987) and Hsieh, 1988, Hsieh, 1989. Baillie and Bollerslev (1991) used a GARCH model for intra-day rates; subsequently Baillie, Bollerslev and Mikkelson (1996) developed a fractionally integrated GARCH model. Cecen and Erkal (1996) argue that inconsistencies

Out of sample forecasting accuracy

For all data sets, one to ten periods ahead forecasts were produced for the final third of each data set, as defined in Table 1. Initially, the analysis concentrates on one period ahead forecasts. The forecast errors are described by summary accuracy measures and significance tests to evaluate relative accuracy are performed where possible.

Conclusion

The concept of forecasting accuracy has been examined empirically with different frequencies of FX data using forecasting methods based on the assumptions of either a linear or non-linear generating process. The measurement of point accuracy was achieved using a range of summary statistics coupled with tests of significance. The significance of directional accuracy was measured using Peseran and Timmerman’s test and the associated theoretical profit assessed by simple trading rules.

The error

Biography: Nigel MEADE is Reader in Management Science at the Management School, Imperial College, University of London. His research interests are statistical model building in general and applied time series analysis and forecasting in particular. He is an associate editor of the International Journal of Forecasting.

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