Intraday foreign exchange rate forecasting using sparse grids

We present a machine learning approach using the sparse grid combination technique for the forecasting of intraday foreign exchange (fx) rates. The aim is to learn the impact of trading rules used by technical analysts just from the empirical behaviour of the market. To this end, the problem of analyzing a time series of transaction tick data is transformed by delay embedding into a D-dimensional regression problem using derived measurements from several different exchange rates. Then, a grid-based approach is used to discretize the resulting high-dimensional feature space. To cope with the curse of dimensionality we employ sparse grids in the form of the combination technique. Here, the problem is discretized and solved for a collection of conventional grids. The sparse grid solution is then obtained by linear combination of the solutions on these grids. We give the results of this approach to fx forecasting using real historical exchange data of the Euro, the US dollar, the Japanese Yen, the Swiss Franc and the British Pound from 2001 to 2005.