Change Point Detection for Non-Stationary and Cross-Correlated Time Series
Add mean shifts to multivariate time series data
Apply Thresholding to VAR Coefficients
Compute VAR Model Residuals
Cross Validation for Elastic Net VAR Estimation
Cross-Validated VAR Estimation using Elastic Net
Construct Lagged Design Matrix for VAR
Estimate the fluctuating mean sequence via maximum likelihood
Estimate fluctuating mean segmentwise given detected change points
Robust parameter estimation (RPE) for multivariate time series
Robust parameter estimation (RPE) for univariate time series
Estimate Covariance Matrix from Residuals
Estimate non-diagonal VAR(1) parameters after mean removal
Fit VAR Model with Elastic Net via Cross Validation
Core change point detection algorithm (given known parameters)
FluxPoint change point detection algorithm
Generate multivariate time series from the proposed model
Evaluate change point detection accuracy metrics
Approximate the long-run covariance matrix $\Gamma_{\boldsymbol{\epsil...
Compute the covariance matrix for observatio...
Matrix inverse
Objective function for robust parameter estimation (RPE)
Plot multivariate time series with detected change points and estimate...
Randomly generate an autoregressive coefficient matrix
Randomly generate an innovation covariance matrix $\Sigma_{\boldsymbol...
Split Coefficient Matrix into VAR Lags
Matrix square root
Transform Data for VAR Estimation
Implements methods for multiple change point detection in multivariate time series with non-stationary dynamics and cross-correlations. The methodology is based on a model in which each component has a fluctuating mean represented by a random walk with occasional abrupt shifts, combined with a stationary vector autoregressive structure to capture temporal and cross-sectional dependence. The framework is broadly applicable to correlated multivariate sequences in which large, sudden shifts occur in all or subsets of components and are the primary targets of interest, whereas small, smooth fluctuations are not. Although random walks are used as a modeling device, they provide a flexible approximation for a wide class of slowly varying or locally smooth dynamics, enabling robust performance beyond the strict random walk setting.