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Journal Article
CLT FOR LARGEST EIGENVALUES AND UNIT ROOT TESTING FOR HIGH-DIMENSIONAL NONSTATIONARY TIME SERIES
2018
Overview
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
Y
t
j
=
∑
k
=
0
∞
b
k
Z
t
−
k
,
j
with
∑
i
=
0
∞
|
b
i
|
<
∞
. Consider a p-dimensional time series model of the form xt = ∏xt−1 + ∑1/2yt, 1 ≤ t ≤ T with yt = (Y
t1, … , Ytp
)′ and ∑1/2 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.
Publisher
Institute of Mathematical Statistics
Subject
