Forecasting Symmetric Random Walks: A Fusion Approach

Forecasting random walks is notoriously challenging, with na\"ive prediction serving as a difficult-to-surpass baseline. To investigate the potential of using movement predictions to improve point forecasts in this context, this study focuses on symmetric random walks, in which the target variable's future value is reformulated as a combination of its future movement and current value. The proposed forecasting method, termed the fusion of movement and na\"ive predictions (FMNP), is grounded in this reformulation. The simulation results show that FMNP achieves statistically significant improvements over na\"ive prediction, even when the movement prediction accuracy is only slightly above 0.50. In practice, movement predictions can be derived from the comovement between an exogenous variable and the target variable and then linearly combined with the na\"ive prediction to generate the final forecast. FMNP effectiveness was evaluated on four U.S. financial time series -- the close prices of Boeing (BA), Brent crude oil (OIL), Halliburton (HAL), and Schlumberger (SLB) -- using the open price of the Financial Times Stock Exchange (FTSE) index as the exogenous variable. In all the cases, FMNP outperformed the na\"ive prediction, demonstrating its efficacy in forecasting symmetric random walks and its potential applicability to other forecasting tasks.