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.

中文翻译：

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基于距离的最近邻预测及其在汇率可预测性中的应用

预测非平稳时间序列，尤其是在数据生成过程包含随机游走分量时，是一项困难的任务，有时甚至是不可能的任务。在本文中，我们建议使用基于距离的最近邻居（NN）来预测上述类型的时间序列的直观，计算快速且便捷的方式。我们利用了随机游走模型中存在的路径和规模依赖关系，因此我们提供了许多理论结果（a）用于选择NN的距离，（b）一些使用这些距离的新预测模型（c）所得预测的性质。我们通过对汇率和商品的时间序列进行全面的经验应用来说明我们方法的有效性，