Limit Theory for an Explosive Autoregressive Process

Xiaohu Wang () and Jun Yu
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Xiaohu Wang: Chinese University of Hong Kong

No 08-2013, Working Papers from Singapore Management University, School of Economics

Abstract: Large sample properties are studied for a rst-order autoregression (AR(1)) with a root greater than unity. It is shown that, contrary to the AR coe¢ cient, the least- squares (LS) estimator of the intercept and its t-statistic are asymptotically normal without requiring the Gaussian error distribution, and hence an invariance principle applies. While the invariance principle does not apply to the asymptotic distribution of the LS estimator of the AR coe¢ cient, we show explicitly how it depends on the initial condition and the intercept. Also established are the asymptotic independence between the LS estimators of the intercept and the AR coefficient and the asymptotic independence between their t-statistics. Asymptotic theory for explosive processes is compared to that for unit root AR(1) processes and stationary AR(1) processes. The coefficient based test and the t test have better power for testing the hypothesis of zero intercept in the explosive process than in the stationary process.

Pages: 19 pages
Date: 2013-11
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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Citations: View citations in EconPapers (1)

Published in SMU Economics and Statistics Working Paper Series

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Journal Article: Limit theory for an explosive autoregressive process (2015)
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