Projects per year
Abstract
Let {Z_{ij}} be independent and identically distributed (i.i.d.) random variables with EZ_{ij} = 0, EZ_{ij}^{2} = 1 and EZ_{ij}^{4} < ∞. Define linear processes Y_{tj} =^{∞} _{k}=_{0} b_{k}Z_{t}−_{k,j} with^{∞} _{i}=_{0} b_{i} < ∞. Consider a pdimensional time series model of the form x_{t} = x_{t} _{−1} +^{1}/^{2}yt, 1 ≤ t ≤ T with yt = (Y_{t}1, . . ., Y_{tp}) and^{1}/^{2} be the square root of a symmetric positive definite matrix. Let B = (1/p)XX^{∗} with X = (x_{1}, . . ., x_{T}) 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 x_{t} is nonstationary. As an application, two new unit root tests for possible nonstationarity of highdimensional time series are proposed and then studied both theoretically and numerically.
Original language  English 

Pages (fromto)  21862215 
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

Econometric Model Building and Estimation: Theory and Practice
Australian Research Council (ARC), Monash University
1/01/17 → 31/12/20
Project: Research

Non and SemiParametric Panel Data Econometrics: Theory and Applications
Gao, J. & Phillips, P.
Australian Research Council (ARC), Monash University, Yale University
1/01/15 → 31/12/19
Project: Research