Large sample properties are studied for a Örst-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. The coe¢ cient 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.
Wang, Xiaohu and YU, Jun.
Limit Theory for an Explosive Autoregressive Process. (2013). Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1513
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