Traditional methods for point forecasting in univariate random walks often fail to surpass naive benchmarks due to data unpredictability. This study introduces a novel forecasting method that fuses movement prediction (binary classification) with naive forecasts for accurate one-step-ahead point forecasting. The method's efficacy is demonstrated through theoretical analysis, simulations, and real-world data experiments. It reliably exceeds naive forecasts with movement prediction accuracies as low as 0.55, outperforming baseline models like ARIMA, linear regression, MLP, and LSTM networks in forecasting the S\&P 500 index and Bitcoin prices. This method is particularly advantageous when accurate point predictions are challenging but accurate movement predictions are attainable, translating movement predictions into point forecasts in random walk contexts.

翻译：传统单变量随机游走点预测方法常因数据不可预测性而难以超越朴素基准。本研究提出一种新颖的预测方法，将运动预测（二元分类）与朴素预测相融合，以实现精确的一步超前点预测。通过理论分析、仿真实验和真实数据验证，证明了该方法的有效性。在运动预测准确率低至0.55的情况下，该方法仍能可靠地超越朴素预测，并在标普500指数和比特币价格预测中优于ARIMA、线性回归、MLP及LSTM网络等基线模型。该方法在精确点预测困难但准确运动预测可行时具有显著优势，实现了随机游走背景下运动预测向点预测的转化。