Improvements to surrogate data methods for nonstationary time series

Area of Science:

• Time Series Analysis
• Nonlinear Dynamics
• Statistical Hypothesis Testing

Background:

• Surrogate data methods are crucial for testing system linearity using single time series realizations.
• Classical methods preserve linear stochastic structure and amplitude distribution but fail with non-stationary data, particularly trends.
• Existing modifications struggle with trend preservation and introduce artifacts due to Fourier transform constraints.

Purpose of the Study:

• To propose a simple technique for generating surrogate data that preserves trends and avoids end-matching artifacts.
• To enhance the reliability of hypothesis testing for system linearity in the presence of non-stationarity.
• To demonstrate the advantages of the proposed method over classical approaches.

Main Methods:

• Developed a technique integrated with existing Fourier-transform-based surrogate data methods.
• The method jointly preserves linear stochastic structure, amplitude distribution, and trends (global non-stationarity).
• Avoids issues related to end mismatch in Fourier transform applications.

Main Results:

• Successfully generated surrogate data that accurately reflects the trend of original non-stationary time series.
• The proposed technique overcomes limitations of classical and modified surrogate data methods.
• Demonstrated superior performance using artificial and real-world stationary and non-stationary time series.

Conclusions:

• The proposed technique offers a robust solution for creating trend-preserving surrogate data.
• This advancement improves the accuracy of linearity hypothesis testing for complex time series.
• The method is broadly applicable to various stationary and non-stationary time series analyses.