  Time series forecasting represents a significant and challenging task across
various fields. Recently, methods based on mode decomposition have dominated
the forecasting of complex time series because of the advantages of capturing
local characteristics and extracting intrinsic modes from data. Unfortunately,
most models fail to capture the implied volatilities that contain significant
information. To enhance the prediction of contemporary diverse and complex time
series, we propose a novel time series forecasting paradigm that integrates
decomposition with the capability to capture the underlying fluctuation
information of the series. In our methodology, we implement the Variational
Mode Decomposition algorithm to decompose the time series into K distinct
sub-modes. Following this decomposition, we apply the Generalized
Autoregressive Conditional Heteroskedasticity (GARCH) model to extract the
volatility information in these sub-modes. Subsequently, both the numerical
data and the volatility information for each sub-mode are harnessed to train a
neural network. This network is adept at predicting the information of the
sub-modes, and we aggregate the predictions of all sub-modes to generate the
final output. By integrating econometric and artificial intelligence methods,
and taking into account both the numerical and volatility information of the
time series, our proposed framework demonstrates superior performance in time
series forecasting, as evidenced by the significant decrease in MSE, RMSE, and
MAPE in our comparative experimental results.
