Neural Network Smoothing in Correlated Time Series Context.

Area of Science:

• Time Series Analysis
• Machine Learning
• Signal Processing

Background:

• Non-parametric trend estimation is crucial for understanding time series data.
• Existing methods may struggle with complex temporal dependencies.
• Neural networks offer a flexible framework for complex data modeling.

Purpose of the Study:

• To develop a novel neural network (NN) smoothing architecture for non-parametric time series trend estimation.
• To introduce a regularization parameter (lambda) for controlling time domain smoothing.
• To propose a criterion for selecting the optimal regularization parameter.

Main Methods:

• A neural network smoother architecture is proposed.
• The method computes trends in the state domain and minimizes a cost function.
• A regularization term, penalized by lambda, is incorporated to enforce time domain smoothing.
• A selection criterion is defined to determine the optimal lambda value.

Main Results:

• The NN-smoother effectively estimates the trend of time series data.
• The regularization parameter lambda controls the degree of smoothing.
• The proposed selection criterion is proven to be an unbiased approximation of the mean squared averaged error under specific conditions.

Conclusions:

• The developed NN-smoother provides an effective method for non-parametric time series trend estimation.
• The regularization parameter selection criterion ensures optimal smoothing performance.
• This approach is particularly suitable for time series with zero-mean, auto-correlated, and stationary noise components.