We present a machine learning approach for the forecasting of time series using the sparse grid combination technique. In this approach, the problem of analyzing a time series is first transformed into a higher-dimensional regression problem based on a delay embedding of the empirical data. Then, a grid-based approach is used to discretize the resulting high-dimensional feature space. In order to cope with the curse of dimensionality, we employ sparse grids in the form of the combination technique. Here, the regression problem is discretized and solved for a sequence of conventional grids with varying mesh widths. The sparse grid solution is then obtained by a linear combination of the solutions on these grids. We present the results of this approach for forecasting a benchmark time series and intraday foreign exchange rates using historical exchange data of several currencies.