Abstract
This paper proposes a new near-unit root test for a class of high-dimensional nonstationary time series. A central limit theorem for the proposed test is proposed and then evaluated by an extensive simulation study.
Highlights
There is a long literature about testing unit–root time series
Another contribution of this paper is that it develops a new near unit root test
From the main theoretical results of [31], we find that when φ = 1, the largest eigenvalues of B depend on aitr(Σ) and ai tr(Σ2), which can be estimated
Summary
There is a long literature about testing unit–root time series. Several testing methods have been proposed for testing near unit root time series. Pan and Gao [31] may be the first paper to deal with the largest eigenvalues of sample covariance matrices generated from high–dimensional nonstationary time series data. This paper establishes the asymptotic behaviour of the first k largest eigenvalues of the sample covariance matrices of the time series model with near unit root. Another contribution of this paper is that it develops a new near unit root test.
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