The k‐nearest neighbors algorithm is one of the prominent techniques used in classification and regression. Despite its simplicity, the k‐nearest neighbors has been successfully applied in time series forecasting. However, the selection of the number of neighbors and feature selection is a daunting task. In this paper, we introduce two methodologies for forecasting time series that we refer to as Classical Parameters Tuning in Weighted Nearest Neighbors and Fast Parameters Tuning in Weighted Nearest Neighbors. The first approach uses classical parameters tuning that compares the most recent subsequence with every possible subsequence from the past of the same length. The second approach reduces the neighbors' search set, which leads to significantly reduced grid size and hence a lower computational time. To tune the models' parameters, both methods implement an approach inspired by cross‐validation for weighted nearest neighbors. We evaluate the forecasting performance and accuracy of our models. Then, we compare them to other approaches, especially, Seasonal Autoregressive Integrated Moving Average, Holt Winters, and Exponential Smoothing State Space Model. Real data examples on retail and food services sales in the United States and milk production in the United Kingdom are analyzed to demonstrate the application and efficiency of the proposed approaches.

中文翻译：

---

将 k 最近邻应用于时间序列预测：两种新方法

这k‐最近邻算法是分类和回归中使用的重要技术之一。尽管它很简单，k‐最近邻已成功应用于时间序列预测。然而，邻居数量的选择和特征的选择是一项艰巨的任务。在本文中，我们介绍了两种预测时间序列的方法，我们将其称为加权最近邻中的经典参数调整和加权最近邻中的快速参数调整。第一种方法使用经典的参数调整，将最近的子序列与过去相同长度的每个可能的子序列进行比较。第二种方法减少了邻居的搜索集，从而显着减小了网格大小，从而缩短了计算时间。为了调整模型的参数，两种方法都实现了一种受加权最近邻交叉验证启发的方法。我们评估模型的预测性能和准确性。然后，我们将它们与其他方法进行比较，特别是季节性自回归积分移动平均、Holt Winters 和指数平滑状态空间模型。对美国零售和食品服务销售以及英国牛奶生产的真实数据示例进行分析，以证明所提出方法的应用和效率。