High-dimensional time series segmentation via factor-adjusted vector autoregressive modelling

TL;DR

This paper introduces a novel piecewise stationary time series model that combines factor structures and VAR models to effectively handle high-dimensional data with strong correlations and structural changes, improving change point detection.

Contribution

It proposes a two-stage segmentation method for high-dimensional time series with strong correlations, with proven consistency in estimating change points under general conditions.

Findings

Method performs well on simulated data

Effective in detecting change points in stock data

Handles strong serial and cross-sectional correlations

Abstract

Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with the dimensionality which necessitates the sparsity assumption in high dimensions. However, it is debatable whether such an assumption is adequate for handling datasets exhibiting strong serial and cross-sectional correlations. We propose a piecewise stationary time series model that simultaneously allows for strong correlations as well as structural changes, where pervasive serial and cross-sectional correlations are accounted for by a time-varying factor structure, and any remaining idiosyncratic dependence between the variables is handled by a piecewise stationary VAR model. We propose an accompanying two-stage data segmentation methodology which fully addresses the challenges arising from the latency of the component processes. Its consistency in estimating both the total number and the locations of the change points in the latent components, is established under conditions considerably more general than those in the existing literature. We demonstrate the competitive performance of the proposed methodology on simulated datasets and an application to US blue chip stocks data.