Modeling High-Dimensional Unit-Root Time Series
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In this paper, we propose a new procedure to build a structural-factor model for a vector unit-root time series. For a p-dimensional unit-root process, we assume that each component consists of a set of common factors, which may be unit-root non-stationary, and a set of stationary components, which contain the cointegrations among the unit-root processes. To further reduce the dimensionality, we also postulate that the stationary part of the series is a nonsingular linear transformation of certain common factors and idiosyncratic white noise components as in Gao and Tsay (2019a, b). The estimation of linear loading spaces of the unit-root factors and the stationary components is achieved by an eigenanalysis of some nonnegative definite matrix, and the separation between the stationary factors and the white noises is based on an eigenanalysis and a projected principal component analysis. Asymptotic properties of the proposed method are established for both fixed p and diverging p as the sample size n tends to infinity. Both simulated and real examples are used to demonstrate the performance of the proposed method in finite samples.
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