Distance-based nearest neighbour forecasting with application to exchange rate predictability

Forecasting non-stationary time series, especially when the data generating processes contains a random walk component, is a difficult and sometimes impossible task. In this paper we suggest an intuitive, computationally fast and expedient way of forecasting time series of the above type using distance-based nearest neighbours (NN). We exploit to advantage the path and scale dependence present in a random walk model and so we provide a number of theoretical results (a) on the distances used for selecting the NN, (b) on a number of new forecasting models that use these distances and (c) on the properties of the resulting forecasts. We illustrate the efficacy of our method via a comprehensive empirical application on time series of exchange rates and commodities, where we present the resulting performance enhancements and discuss the importance of such results in a decision-making context, linking our forecasting approach with management mathematics and predictive analytics problems.