Wavelet Decomposition Combined with Autoregressive Linear Model for Predictive Analysis

This article provides an in-depth exploration of a hybrid forecasting approach that combines wavelet decomposition with autoregressive linear models. This methodology enables enhanced understanding and prediction of time series data patterns. We demonstrate the complete implementation using MATLAB source code, detailing key functions like wavedec for wavelet decomposition and arima for autoregressive modeling.

To fully comprehend this approach, fundamental knowledge of both wavelet decomposition and autoregressive linear models is essential. Wavelet decomposition serves as a mathematical tool for signal characterization, breaking down signals into components across different frequency bands and temporal scales using algorithms like discrete wavelet transform (DWT). Autoregressive linear models provide a statistical framework for time series modeling, effectively capturing sequential dependencies through lagged variable relationships.

The integration of these methods creates a powerful forecasting framework. Through wavelet decomposition implemented via MATLAB's Wavelet Toolbox functions, time series data is decomposed into multi-resolution components. Subsequently, autoregressive models are applied to each component using system identification tools, establishing relationships between decomposed elements. This dual approach significantly improves prediction accuracy by addressing both frequency-domain characteristics and temporal correlations.

Our implementation includes step-by-step MATLAB code demonstrating: 1) Signal preprocessing and wavelet transformation using wavedec function, 2) Component-specific autoregressive model fitting with arima estimation, and 3) Forecast recombination techniques. This practical guide enables researchers to apply this advanced methodology to various time series forecasting scenarios.