A Combination Model Based on Sequential General Variational Mode Decomposition Method for Time Series Prediction

TL;DR

The paper addresses forecasting non-stationary financial time series by introducing SGVMD-ARIMA and SGVMD-E-ARIMA, a decomposition-based approach that uses Sequential General Variational Mode Decomposition to extract trend and AM-FM components and forecast them with ARIMA (or envelope ARIMA for AM-FM parts). It proposes the SGVMD framework (building on GVMD and VMD) with a constrained loss to enable sequential, unknown-mode extraction, and two prediction pathways for the components. Through experiments on online store sales and Australian beer production, the SGVMD-ARIMA and SGVMD-E-ARIMA models outperform single models (ARIMA, Holt-Winters, LSTM) and EMD-based hybrids, often by substantial margins. The results demonstrate improved accuracy and robustness for non-stationary, non-linear time series, suggesting broad applicability to economic forecasting and related domains.

Abstract

Accurate prediction of financial time series is a key concern for market economy makers and investors. The article selects online store sales and Australian beer sales as representatives of non-stationary, trending, and seasonal financial time series, and constructs a new SGVMD-ARIMA combination model in a non-linear combination way to predict financial time series. The ARIMA model, LSTM model, and other classic decomposition prediction models are used as control models to compare the accuracy of different models. The empirical results indicate that the constructed combination prediction model has universal advantages over the single prediction model and linear combination prediction model of the control group. Within the prediction interval, our proposed combination model has improved advantages over traditional decomposition prediction control group models.

Figures (6)

• Figure 1: Modal components and their upper and lower envelope lines and prediction results of each envelope line. And the prediction results of AM-FM components.
• Figure 2: Prediction results of AM-FM components.
• Figure 3: Time series plot of experimental data for Example A and the results of IMF component analysis for the Example A. And Optimized prediction results for each AM-FM component.
• Figure 4: Comparison for models in example A.
• Figure 5: The time series plot of Australian beer production with the results of principal IMF analysis for this Example.