Projects per year
Abstract
Let {Zij} be independent and identically distributed (i.i.d.) random variables with EZij = 0, E|Zij|2 = 1 and E|Zij|4 < ∞. Define linear processes Ytj =∞ k=0 bkZt−k,j with∞ i=0 |bi| < ∞. Consider a p-dimensional time series model of the form xt = xt −1 +1/2yt, 1 ≤ t ≤ T with yt = (Yt1, . . ., Ytp) and1/2 be the square root of a symmetric positive definite matrix. Let B = (1/p)XX∗ with X = (x1, . . ., xT) and X∗ be the conjugate transpose. This paper establishes both the convergence in probability and the asymptotic joint distribution of the first k largest eigenvalues of B when xt is nonstationary. As an application, two new unit root tests for possible nonstationarity of high-dimensional time series are proposed and then studied both theoretically and numerically.
Original language | English |
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Pages (from-to) | 2186-2215 |
Number of pages | 30 |
Journal | Annals of Statistics |
Volume | 46 |
Issue number | 5 |
DOIs | |
Publication status | Published - Oct 2018 |
Keywords
- Asymptotic normality
- Largest eigenvalue
- Linear process
- Unit root test
Projects
- 2 Finished
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Econometric Model Building and Estimation: Theory and Practice
Gao, J. (Primary Chief Investigator (PCI))
Australian Research Council (ARC), Monash University
1/01/17 → 31/12/20
Project: Research
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Non- and Semi-Parametric Panel Data Econometrics: Theory and Applications
Gao, J. (Primary Chief Investigator (PCI)) & Phillips, P. (Partner Investigator (PI))
Australian Research Council (ARC), Monash University, Yale University
1/01/15 → 31/12/19
Project: Research