Limit theory for mildly integrated process with intercept
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...
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2018
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| Online Access: | https://ink.library.smu.edu.sg/soe_research/2169 https://ink.library.smu.edu.sg/context/soe_research/article/3169/viewcontent/limit_theory.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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 t-test for both of them keeping valid. Empirical implication of these limit theory is also discussed. |
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