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Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Stationarity assumption is often unrealistic for real-world time series.
  • Piecewise stationarity, allowing for model changes at multiple change points, offers a more realistic framework.
  • High-dimensional data presents unique challenges for change point detection and parameter estimation.

Purpose of the Study:

  • To develop a robust method for simultaneously estimating change points and parameters in high-dimensional piecewise vector autoregressive (VAR) models.
  • To address the limitations of traditional stationarity assumptions in time series analysis.
  • To provide a reliable procedure for complex, evolving datasets.

Main Methods:

  • A three-stage procedure combining penalized least squares with a total variation penalty for initial change point estimation.
  • Reformulation of change point detection as a high-dimensional variable selection problem.
  • Development of a selection criterion to refine over-estimated change points and subsequent segment-wise VAR parameter estimation.

Main Results:

  • The proposed method consistently detects the number and location of change points.
  • Accurate and consistent estimation of VAR parameters within identified segments.
  • Demonstrated effectiveness through simulations and real-world data applications.

Conclusions:

  • The developed procedure offers a statistically sound and effective approach for analyzing piecewise stationary time series.
  • It overcomes challenges associated with high dimensionality and multiple change points.
  • Provides a valuable tool for researchers and practitioners dealing with dynamic time series data.