Forecasting is essential for optimizing resource allocation, particularly during crises such as the unprecedented COVID-19 pandemic. This paper focuses on developing an algorithm for generating k-step-ahead interval forecasts for autoregressive time series. Unlike conventional methods that assume a fixed distribution, our approach utilizes kernel distribution estimation to accommodate the unknown distribution of prediction errors. This flexibility is crucial in real-world data, where deviations from normality are common, and neglecting these deviations can result in inaccurate predictions and unreliable confidence intervals. We evaluate the performance of our method through simulation studies on various autoregressive time series models. The results show that the proposed approach performs robustly, even with small sample sizes, as low as 50 observations. Moreover, our method outperforms traditional linear model-based prediction intervals and those derived from the empirical distribution function, particularly when the underlying data distribution is non-normal. This highlights the algorithm’s flexibility and accuracy for interval forecasting in non-Gaussian contexts. We also apply the method to log-transformed weekly COVID-19 case counts from lower-middle-income countries, covering the period from June 1, 2020, to March 13, 2022.