Fusion of Movement and Naive Predictions for Point Forecasting in Univariate Random Walks

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.