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

arXiv: https://arxiv.org/abs/1711.07357 · HTML: https://mlsanity.com/paper/1711.07357/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2017.

## Built on by (most cited first, 9 of 9)

- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [CP-PINNs: Data-Driven Changepoints Detection in PDEs Using Online Optimized Physics-Informed Neural Networks](https://mlsanity.com/paper/2208.08626/) (2022)
- [Causal Discovery-Driven Change Point Detection in Time Series](https://mlsanity.com/paper/2407.07290/) (2024)
- [Causal Discovery in High-Dimensional Point Process Networks with Hidden Nodes](https://mlsanity.com/paper/2109.10947/) (2021)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Detection and Estimation of Structural Breaks in High-Dimensional Functional Time Series](https://mlsanity.com/paper/2304.07003/) (2023)
- [Jacobian Granger Causal Neural Networks for Analysis of Stationary and Nonstationary Data](https://mlsanity.com/paper/2205.09573/) (2022)
- [A Generalized Adaptive Joint Learning Framework for High-Dimensional Time-Varying Models](https://mlsanity.com/paper/2601.04499/) (2026)
- [Dynamic Elliptical Graph Factor Models via Riemannian Optimization with Geodesic Temporal Regularization](https://mlsanity.com/paper/2605.18316/) (2026)

## Abstract (arXiv)

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for consistent estimation of both structural change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and propose a penalized least square estimator using a total variation penalty. We show that the proposed penalized estimation method over-estimates the number of change points. We then propose a backward selection criterion in conjunction with a penalized least square estimator to tackle this issue. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number of change points and their locations. We also show that the procedure consistently estimates the VAR parameters. The performance of the method is illustrated through several simulation scenarios and real data examples.