Time series forecast intervals using circular bootstrapped training simulation with invariant distance KNN

This paper presents a nonparametric interval forecasting method that combines circular block bootstrap resampling with complexity-invariant <em>K</em>-nearest-neighbor time-series prediction. Prediction intervals are obtained directly from bootstrap-resampled training series, thereby preserving temporal dependence while accounting for forecast uncertainty. Under weak dependence and local stability assumptions, asymptotic validity of the resulting prediction intervals is established. The proposed method is evaluated using twelve time-series datasets drawn from economic, environmental, industrial, and energy applications. Empirical performance is compared with seasonal autoregressive integrated moving average models and long short-term memory neural networks using the mean absolute percentage error, empirical coverage probability, and interval score. The results show that the proposed approach yields prediction intervals of moderate width with competitive forecasting accuracy across most datasets, while empirical coverage remains close to the nominal level. Mild undercoverage is observed in short samples, attributable to limited data availability and fixed tuning parameters.