Application of the seasonal holt-winters model to study exchange rate volatility

Abstract

The paper proposes a new approach to investigating the dynamics of hourly exchange rates of two currencies – the Euro (EUR) and US dollar (USD). The dynamics of foreign exchange (forex) rate is a complex process that can be better understood through a study of its characteristics, such as for instance volatility. In this article the exchange rate fluctuation is analysed by calculating the sum of absolute differences (SAD) of a time series per hour. It has been shown empirically that a new time series constructed from SAD values is more suitable for predicting exchange rate volatility if it takes into account only the magnitude of the exchange rate fluctuation and ignores its direction. The analysis of EUR/USD exchange rate data at major financial centers has revealed that both exchange rates undergo periodical intraday variations; therefore, both additive and multiplicative versions of Holt-Winters exponential smoothing techniques have been applied in the analysis and predict of exchange rate volatility. These methods are appropriate for a time series with a linear trend and seasonal variations. Since a time series of SAD values does not have a clear trend, simplified versions (without changes in trend) of the Holt-Winters model were applied. Two different statistics - mean absolute error (MAE) and root mean squared error (RMSE) - were applied to select the optimal parameters of four versions of the Holt-Winters model. The study showed that volatility is best predicted by a simplified version of the multiplicative Holt-Winters model.