Movement-Prediction-Adjusted Naive Forecast

In financial time series forecasting, surpassing the naive forecast is challenging due to the randomness in the data. To address this challenge, this study proposes a novel forecast combination method, the movement-prediction-adjusted naive forecast (MPANF), which is designed to improve point forecasts beyond the naive baseline. Specifically, MPANF integrates two forecasting components: a naive forecast and a movement prediction. The final forecast is generated by adjusting the naive forecast with a movement prediction term, the weight of which is the product of two in-sample quantities: one is a coefficient determined from the movement prediction accuracy and the other is the mean absolute increment. The performance of MPANF was evaluated on eight financial time series via standard metrics, including the RMSE, MAE, MAPE, and sMAPE. Under modest movement prediction accuracy slightly above 0.55, MPANF generally outperforms common benchmarks such as the naive forecast, naive forecast with drift, integrated moving average of order (1,1) (IMA(1,1)), and linear regression. These findings suggest that MPANF can serve as an effective second-stage method when reliable movement predictions are available.