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Mild-Explosive And Local-To-Mild-Explosive Autoregressions With Serially Correlated Errors, Yiu Lim Lui, Weilin Xiao, Jun Yu
Mild-Explosive And Local-To-Mild-Explosive Autoregressions With Serially Correlated Errors, Yiu Lim Lui, Weilin Xiao, Jun Yu
Research Collection School Of Economics
This paper firstly extends the results of Phillips and Magdalinos (2007a) by allowing for anti-persistent errors in mildly explosive autoregressive models. It is shown that the Cauchy asymptotic theory remains valid for the least squares (LS) estimator. The paper then extends the results of Phillips, Magdalinos and Giraitis (2010) by allowing for serially correlated errors of various forms in local-to-mild-explosive autoregressive models. It is shown that the result of smooth transition in the limit theory between local-to-unity and mild-explosiveness remains valid for the LS estimator. Finally, the limit theory for autoregression with intercept is developed.
Limit Theory For Mildly Integrated Process With Intercept, Yijie Fei
Limit Theory For Mildly Integrated Process With Intercept, Yijie Fei
Research Collection School Of Economics
Some asymptotic results are given for first-order autoregressive (AR(1)) time series with two features: (i). a nonzero constant intercept (ii). a root moderately deviating from unity. Both stationary and explosive sides are studied. It is shown that the inclusion of intercept will change drastically the large sample properties of the least-squares (LS) estimator obtained in Phillips and Magdalinos (2007, PM hereafter). For near-stationary case, only an unusual convergence of a linear combination of intercept and AR coefficient can be derived. For near-explosive case, on the other hand, the limiting distributions of two estimators will be independent and Gaussian, with conventional …