Fusion of Movement and Naive Predictions for Point Forecasting in Univariate Random Walks (2406.14469v5)

Abstract: Point forecasting in univariate random walks is an important yet challenging research topic. Many attempts at this task often fail to surpass the na\"ive baseline because of the randomness of the data and the improper utilization of exogenous variables as features. In view of the limitations of existing random walk forecasting methods, this study introduces a variant definition of random walks, proposing that point forecasting can be improved beyond the na\"ive baseline through the fusion of movement and na\"ive predictions (FMNP). FMNP naturally bridges movement prediction and point forecasting. It employs an exogenous variable to provide a consistent movement prediction for the target variable and uses a linear regression to combine movement and na\"ive predictions. In forecasting five financial time series in the U.S. market with the FTSE opening price as the exogenous variable, FMNP consistently outperforms na\"ive baselines and is superior to baseline models such as ARIMA, MA, MLP, DNN, LSTM, and CNN-LSTM. FMNP 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.