High-dimensional time series segmentation via factor-adjusted vector autoregressive modelling
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Piecewise stationarity is a widely adopted assumption for modelling non-stationary time series. However fitting piecewise stationary vector autoregressive (VAR) models to high-dimensional data is challenging as the number of parameters increases as a quadratic of the dimension. Recent approaches to address this have imposed sparsity assumptions on the parameters of the VAR model, but such assumptions have been shown to be inadequate when datasets exhibit strong (auto)correlations. We propose a piecewise stationary time series model that accounts for pervasive serial and cross-sectional correlations through a factor structure, and only assumes that any remaining idiosyncratic dependence between variables can be modelled by a sparse VAR model. We propose an accompanying two-stage change point detection methodology which fully addresses the challenges arising from not observing either the factors or the idiosyncratic VAR process directly. 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.
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