  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.
