Description

The decomposition-ensemble algorithm, widely used for modeling nonlinear time series data, typically decomposes the target series into oscillation modes, assigning equal weights to all modes for aggregated prediction. However, forecasting performance varies across the decomposed modes due to differences in their characteristics and prediction horizons. This paper introduces a novel decomposition-based model averaging approach that assigns optimized weights to the decomposed modes, thereby enhancing the accuracy of time series forecasts. The proposed model averaging estimator is proven to be asymptotically optimal, achieving the minimum possible quadratic prediction risk. Furthermore, the convergence rates of the estimated weights to the optimal weights, which minimize the expected quadratic loss, are formally established. Simulation studies and empirical applications to stock return forecasting demonstrate the effectiveness of the proposed method.