ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

Area of Science:

• Statistics
• Time Series Analysis
• Signal Processing

Background:

• Replicated nonstationary time series are common in experimental studies.
• Analyzing time-varying frequency patterns in such data presents challenges.
• Existing methods may not adequately capture dynamic group effects.

Purpose of the Study:

• To propose a novel analysis of power (ANOPOW) model for replicated nonstationary time series.
• To enable comparison of time-varying second-order frequency patterns across different groups.
• To estimate group effects as functions of both time and frequency.

Main Methods:

• Development of a locally stationary ANOPOW Cramér spectral representation.
• Bayesian framework utilizing independent two-dimensional second-order random walk (RW2D) priors.
• Piecewise stationary approximation for localized time-varying spectra estimation.
• Integrated Nested Laplace Approximations (INLA) for posterior distribution computation.

Main Results:

• The proposed ANOPOW model effectively analyzes replicated nonstationary time series.
• It allows for flexible and adaptive smoothing of time-varying functional effects.
• Accurate estimation of group effects across time and frequency is achieved.
• The model demonstrates utility in seismic signal and ADHD pupil diameter data analysis.

Conclusions:

• The novel ANOPOW model provides a robust framework for analyzing complex time series data.
• It offers a computationally efficient Bayesian approach using INLA.
• The model is applicable to diverse experimental settings requiring analysis of dynamic group effects.