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Updated: Jul 1, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Published on: December 9, 2015

Modeling Nonstationary Time Series Using Locally Stationary Basis Processes.

Shreyan Ganguly1, Peter F Craigmile2

  • 1Department of Statistics, The Ohio State University, Columbus, Ohio, USA.

Journal of Time Series Analysis
|June 30, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces locally stationary processes for improved time series analysis when stationarity is not met. These models offer more accurate uncertainty quantification than traditional stationary methods.

Keywords:
62M1062M15EEGcausalityparameter estimationtests of stationaritytime-varying processesuncertainty quantification

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Last Updated: Jul 1, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Area of Science:

  • Statistics
  • Time Series Analysis
  • Signal Processing

Background:

  • Classical time series analysis relies on stationary models, which are often unrealistic in practice.
  • The assumption of stationarity can lead to inaccurate uncertainty quantification for many real-world time series.
  • Many time series exhibit time-varying parameters, deviating from strict stationarity.

Purpose of the Study:

  • To define and develop methods for analyzing locally stationary processes.
  • To improve uncertainty quantification in time series analysis by relaxing the stationarity assumption.
  • To provide a framework for parameter estimation and hypothesis testing for non-stationary time series.

Main Methods:

  • Defined a class of locally stationary processes with time-varying parameters.
  • Parameterized time-varying parameters using a transformation of basis functions.
  • Developed parameter estimation methods and a statistical test for departures from stationarity.
  • Validated methods through simulation studies and applied them to electroencephalogram (EEG) data.

Main Results:

  • Locally stationary models provide more accurate uncertainty quantification compared to assuming stationarity.
  • The proposed methods enable effective parameter estimation for time-varying models.
  • The developed test can detect departures from stationarity in time series data.
  • Demonstrated the practical utility of the methods on an electroencephalogram time series.

Conclusions:

  • Locally stationary processes offer a more realistic and accurate approach to time series analysis.
  • The developed methods enhance the reliability of uncertainty quantification in non-stationary settings.
  • This framework is applicable to various fields requiring analysis of time-varying data, such as neuroscience.