Movement-Prediction-Adjusted Na\"ive Forecast

This study introduces a movement-prediction-adjusted na\"ive forecast for time series exhibiting symmetric random walk characteristics, which is applicable after accurate movement predictions are available. Specifically, the original na\"ive forecast is adjusted by a weighted movement prediction term, where the weights are determined via two parameters derived from the in-sample data: one based on directional accuracy of the movement prediction and the other on the mean absolute increment of the target series. Simulation experiments were conducted across four types of synthetic symmetric random walk series, each with different variance structures. For each time series, diverse movement predictions with predefined directional accuracies were randomly generated, and the resulting forecasts were evaluated via the RMSE, MAE, MAPE, and sMAPE metrics. The results demonstrated a clear monotonic improvement in the forecast performance as the directional accuracy increased. Notably, the adjusted na\"ive forecast achieved statistically significant improvements even at relatively low directional accuracy levels slightly above 0.50. These findings imply that the movement-prediction-adjusted na\"ive forecast can serve as an effective second-stage method for forecasting symmetric random walk time series when consistent and accurate movement predictions are provided.