Time Series Signal Prediction Using Wavelet Neural Network Transformation

Wavelet Neural Networks (WNNs) combine the advantages of wavelet transforms and neural networks, providing an effective approach for time series signal prediction. The wavelet transform decomposes signals multi-scale in the time-frequency domain, capturing characteristics at different resolutions, while neural networks learn these features to construct predictive models. Code implementation typically involves using wavelet decomposition functions (e.g., PyWavelets' `wavedec` in Python) to generate approximation and detail coefficients, followed by feeding these components into neural network layers.

In time series forecasting, WNNs first perform wavelet decomposition on input signals to extract feature components from different frequency bands. These components are then input into neural networks (e.g., MLP or LSTM architectures) for training. This methodology significantly enhances prediction accuracy, particularly excelling in non-stationary and nonlinear signals such as financial data or meteorological records. Key implementation steps include selecting optimal wavelet families (e.g., Daubechies), determining decomposition levels, and configuring network parameters through backpropagation optimization.

Experimental results demonstrate superior performance compared to traditional time series methods like ARIMA or standalone neural networks. Wavelet decomposition excels at extracting local signal features, while neural networks' nonlinear fitting capabilities further refine predictions. This hybrid approach not only improves accuracy but also enhances model robustness, making it suitable for diverse complex time series forecasting scenarios. Implementation typically involves preprocessing signals with `pywt.dwt` for decomposition, normalizing coefficients, and designing neural networks with activation functions like `tanh` or `ReLU` for feature learning.