A Novel Interval Forecast for K-Nearest Neighbor Time Series: A Case Study of Durian Export in Thailand

The k-nearest neighbor (K-NN) time series model is widely favored for its simplicity and ease of understanding. However, it lacks a forecast interval, an essential feature for capturing the uncertainty inherent in point forecasts. This study introduces a novel interval forecasting approach that integrates the K-NN time series model with bootstrapping. A key step involves determining the optimal distribution of K-NN forecasted values, derived from a range of
$k$
values representing the number of nearest neighbors. Considered distributions include Gaussian, gamma, logistic, Weibull, log-normal, Cauchy, inverse-gamma, log-logistic, inverse Weibull, and log-gamma. Forecast values from both recursive and multi-input multi-output (MIMO) K-NN time series techniques are used as inputs in the bootstrapping framework. The proposed forecast intervals are compared with those obtained from the seasonal autoregressive integrated moving average (SARIMA) model, which is a benchmark in statistics. Performance is evaluated using many criteria, such as root mean squared error (RMSE) and average interval width. In a case study of durian exports in Thailand, the results show that the intervals from both recursive- and MIMO-based K-NN forecasts are narrower than those from SARIMA, suggesting increased forecasting confidence. This proposed interval is also applicable to other datasets with trend and/or seasonal components.