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Time series forecasting represents a significant and challenging task acrossvarious fields. Recently, methods based on mode decomposition have dominatedthe forecasting of complex time series because of the advantages of capturinglocal characteristics and extracting intrinsic modes from data. Unfortunately,most models fail to capture the implied volatilities that contain significantinformation. To enhance the prediction of contemporary diverse and complex timeseries, we propose a novel time series forecasting paradigm that integratesdecomposition with the capability to capture the underlying fluctuationinformation of the series. In our methodology, we implement the VariationalMode Decomposition algorithm to decompose the time series into K distinctsub-modes. Following this decomposition, we apply the GeneralizedAutoregressive Conditional Heteroskedasticity (GARCH) model to extract thevolatility information in these sub-modes. Subsequently, both the numericaldata and the volatility information for each sub-mode are harnessed to train aneural network. This network is adept at predicting the information of thesub-modes, and we aggregate the predictions of all sub-modes to generate thefinal output. By integrating econometric and artificial intelligence methods,and taking into account both the numerical and volatility information of thetime series, our proposed framework demonstrates superior performance in timeseries forecasting, as evidenced by the significant decrease in MSE, RMSE, andMAPE in our comparative experimental results.

A novel decomposed-ensemble time series forecasting framework: capturing underlying volatility information