Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models.

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.