Inference for modulated stationary processes.

Area of Science:

• Statistics
• Time Series Analysis

Background:

• Traditional statistical inference methods struggle with non-stationary time series and numerous parameters.
• Existing techniques for stationary or locally stationary time series are inadequate for modulated stationary processes with time-dependent variances.

Purpose of the Study:

• To develop robust statistical inference methods for modulated stationary processes with time-dependent variances.
• To address limitations of existing methods in handling non-stationarity and large parameter spaces.

Main Methods:

• Development of a self-normalization technique to overcome non-stationarity challenges.
• Application of self-normalization for central limit theorem, change-point detection (cumulative sum test), long-run variance estimation, and wild bootstrap.
• Blockwise self-normalization for robust variance estimation.

Main Results:

• Proposed self-normalization methods demonstrate superior performance compared to stationarity-based alternatives in Monte Carlo simulations.
• The methodology effectively handles time series with time-dependent variances and complex parameter structures.

Conclusions:

• Self-normalization provides a powerful framework for statistical inference in modulated stationary processes.
• The developed methods offer improved accuracy and applicability for real-world time series data analysis.