Local powers of least-squares-based test for panel fractional Ornstein-Uhlenbeck process

• Main Authors: TANAKA, Katsuto, XIAO, Weilin, Jun YU
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2020
• Subjects: Panel fractional Ornstein-Uhlenbeck process; Least squares; Asymptotic distribution; Local alternative; Local power; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2358; https://ink.library.smu.edu.sg/context/soe_research/article/3357/viewcontent/LSE_test_14_.pdf
• Institution: Singapore Management University

Based on the least squares estimator, this paper proposes a novel method to test the sign of the persistence parameter in a panel fractional Ornstein-Uhlenbeck process with a known Hurst parameter H. Depending on H ∈ (1/2, 1), H = 1/2, or H ∈ (0, 1/2), three test statistics are considered. In the null hypothesis the persistence parameter is zero. Based on a panel of continuous record of observations, the null asymptotic distributions are obtained when T is fixed and N is assumed to go to infinity, where T is the time span of the sample and N is the number of cross sections. The power function of the tests is obtained under the local alternative where the persistence parameter is close to zero in the order of 1/(T√N). The local power of the proposed test statistics is computed and compared with that of the maximum-likelihood-based test. The hypothesis testing problem and the local power function are also considered when a panel of discrete-sampled observations is available under a sequential limit.