Estimation and Testing for High-Dimensional Near Unit Root Time Series
Bo Zhang (zhangbo890301@outlook.com),
Jiti Gao and
Guangming Pan (gmpan@ntu.edu.sg)
No 12/20, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics
Abstract:
This paper considers a p-dimensional time series model of the form x(t)=Π x(t-1)+Σ^(1/2)y(t), 1≤t≤T, where y(t)=(y(t1),...,y(tp))^T and Σ is the square root of a symmetric positive definite matrix. Here Π is a symmetric matrix which satisfies that ∥Π ∥_2≤ 1 and T(1-∥Π ∥_min) is bounded. The linear processes Y(tj) is of the form ∑_{k=0}^∞b(k)Z(t-k,j) where ∑_{i=0}^∞|b(i)| < ∞ and {Z(ij) } are are independent and identically distributed (i.i.d.) random variables with E Z ij =0, E|Z(ij)|²=1 and E|Z(ij)|^4< ∞. We first investigate the asymptotic behavior of the first k largest eigenvalues of the sample covariance matrices of the time series model. Then we propose a new estimator for the high-dimensional near unit root setting through using the largest eigenvalues of the sample covariance matrices and use it to test for near unit roots. Such an approach is theoretically novel and addresses some important estimation and testing issues in the high-dimensional near unit root setting. Simulations are also conducted to demonstrate the finite-sample performance of the proposed test statistic.
Keywords: asymptotic normality; largest eigenvalue; linear process; near unit root test (search for similar items in EconPapers)
JEL-codes: C21 C32 (search for similar items in EconPapers)
Pages: 40
Date: 2020
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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