Point forecasting in univariate random walks is an important but challenging research topic that has attracted numerous researchers. Unfortunately, traditional regression methods for this task often fail to surpass naive benchmarks due to data unpredictability. From a decision fusion perspective, this study proposes a novel forecasting method, which is derived from a variant definition of random walks, where the random error term for the future value is expressed as a positive random error multiplied by a direction sign. This method, based on the fusion of movement and naive predictions, does not require a loss function for optimization and can be optimized by estimating movement prediction accuracy on the validation set. This characteristic prevents the fusion method from reverting to traditional regression methods and allows it to integrate various machine learning and deep learning models for movement prediction. The method's efficacy is demonstrated through simulations and real-world data experiments. It reliably outperforms naive forecasts with moderate movement prediction accuracies, such as 0.55, and is superior to baseline models such as the 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：单变量随机游走中的点预测是一个重要但具有挑战性的研究课题，吸引了众多研究者。遗憾的是，由于数据的不可预测性，用于此任务的传统回归方法往往难以超越朴素基准。本研究从决策融合的角度提出一种新颖的预测方法，该方法源自随机游走的一种变体定义，其中未来值的随机误差项被表达为正随机误差与方向符号的乘积。这种基于运动预测与朴素预测融合的方法无需优化损失函数，可通过在验证集上估计运动预测准确率进行优化。这一特性防止了融合方法退化为传统回归方法，并使其能够集成各种用于运动预测的机器学习和深度学习模型。通过仿真和真实数据实验验证了该方法的有效性。在运动预测准确率适中（例如0.55）的情况下，该方法能稳定超越朴素预测，并在标普500指数和比特币价格预测中优于ARIMA、线性回归、MLP和LSTM网络等基线模型。当精确点预测难以实现但准确运动预测可行时，该方法在随机游走背景下将运动预测转化为点预测方面具有显著优势。