Testing for unit roots based on sample autocovariances

Heteroskedasticity and autocorrelation consistent covariance matrix estimation

Jinyuan Chang, Guanghui Cheng and Qiwei Yao

Biometrika, 2022, vol. 109, issue 2, 543-550

Abstract: SummaryWe propose a new unit-root test for a stationary null hypothesisagainst a unit-root alternative . Our approach is nonparametric asassumes only that the process concerned is , without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function converges to the finite population autocovariance function for anprocess, but diverges to infinity for a process with unit roots. Therefore, the new test rejectsfor large values of the sample autocovariance function. To address the technical question of how large is large, we split the sample and establish an appropriate normal approximation for the null distribution of the test statistic. The substantial discriminative power of the new test statistic is due to the fact that it takes finite values underand diverges to infinity under . This property allows one to truncate the critical values of the test so that it has asymptotic power 1; it also alleviates the loss of power due to the sample-splitting. The test is implemented in .

Keywords: Autocovariance; Integrated process; Normal approximation; Power-one test; Sample-splitting (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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