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ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

Zeda Li1, Yu Ryan Yue1, Scott A Bruce2

  • 1Baruch College, The City University of New York.

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|March 4, 2024
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Summary
This summary is machine-generated.

This study introduces a new analysis of power (ANOPOW) model for time-varying frequency patterns in nonstationary time series. The model effectively compares group effects over time and frequency, aiding experimental data analysis.

Keywords:
Integrated nested Laplace approximationsLocally stationary ANOPOW Cramér spectral representationPupil diameter time seriesReplicated nonstationary time seriesSpectral analysis

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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.