Journal of Organisational Studies and Innovation
Vol. 1, no.2, Autumn, 2014
Application of ARIMA and ARCH/GARCH models to test the foreign exchange market efficiency
Lucie Ingram
Middlesex University

Abstract: The main purpose of this dissertation is to test the weak form market efficiency of the foreign exchange market. Several analytical methods have been implemented to test the daily and weekly currency returns data. The Augmented Dickey-Fuller, run and serial autocorrelation tests are used to ascertain the presence of random walk. Further analysis is done by comparing time series models including Autoregressive Moving Average (ARMA); Autoregressive Integrated Moving Average (ARIMA); Generalised Autoregressive Conditional Heteroskedasticity (GARCH); Exponential Generalised Autoregressive Conditional Heteroskedasticity (E-GARCH); and GARCH-in-Mean (GARCH-M) models. Maximum Likelihood Estimation (MLE), Log-Likelihood Function (LLF), Akaike’s Information Criterion (AIC) and Ljung-Box Test have been used to examine various models.

The result of our analysis has supported the random walk for all weekly currency pairs.  However, the random walk has not been supported for the daily currency pairs except for pound and dollar (GBP/USD) and euro, dollar (EUR/USD). The actual values compared with the predicted values seem very similar. However, because of the limited scope of this research there is not enough evidence to confirm profitability of trading technique. The presence of ARCH is indicated in the proposition of ARMA (p, q). The ARMA (p, q) for squared returns is equivalent to the GARCH (p, q) for the original series. When comparing the forecasting ability between GARCH and EGARCH model, EGARCH model has been found to be the superior model. Based on the lowest Akaike's Information Criterion for the exchange rates, EGARCH model has outperformed all other models used in the analysis. The possible reason for this is that EGARCH model deals with the asymmetric effect of negative returns over positive returns, a phenomenon typically observed in the foreign exchange markets.

Keywords: efficient market hypothesis, heteroscedasticity, GARCH, exchange range volatility