Time Series Prediction Using Empirical Mode Decomposition and Least Squares Support Vector Machine

Time series prediction constitutes a crucial research direction in data analysis and machine learning, widely applied across finance, meteorology, industrial monitoring, and other domains. The integration of Empirical Mode Decomposition (EMD) with Least Squares Support Vector Machine (LSSVM) presents an effective forecasting methodology, particularly suitable for nonlinear and non-stationary time series data.

EMD serves as an adaptive signal processing technique that decomposes complex time series into multiple Intrinsic Mode Functions (IMFs) and a residual component. This decomposition approach facilitates capturing multi-scale characteristics within time series, providing a clearer data foundation for subsequent predictions. Each IMF component represents fluctuations at different time scales, enabling separate modeling and forecasting for individual components. In MATLAB implementation, the emd() function typically handles this decomposition process, requiring careful consideration of stopping criteria and boundary effects.

Least Squares Support Vector Machine represents an improved version of standard Support Vector Machines, transforming inequality constraints into equality constraints to simplify the solution process. LSSVM demonstrates excellent performance in handling small-sample and nonlinear problems, making it particularly suitable for time series forecasting tasks. Compared to standard SVM, LSSVM achieves faster training speeds while maintaining comparable prediction accuracy. Key MATLAB functions include trainlssvm() for model training and simlssvm() for prediction, with kernel function selection (RBF, linear, polynomial) significantly impacting performance.

In MATLAB implementation, the prediction workflow generally involves these steps: First, perform EMD decomposition on the original time series to obtain multiple IMF components; then establish individual LSSVM prediction models for each IMF component; finally, aggregate the prediction results from all components to generate the final forecast. This divide-and-conquer strategy typically yields superior prediction outcomes compared to direct modeling of the original sequence. Code implementation often involves creating custom functions for component-wise modeling and result integration.

Practical applications require attention to EMD's boundary effect issues and optimization of LSSVM parameters (including kernel function type, regularization parameters, etc.). Cross-validation serves as the common method for determining optimal parameters. Furthermore, to enhance prediction performance, practitioners can integrate additional techniques such as Principal Component Analysis for feature selection or ensemble learning methods for model fusion. MATLAB's optimization toolbox and statistical functions facilitate parameter tuning and model validation processes.