Limit theory for mildly integrated process with intercept

• Main Author: FEI, Yijie
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Autoregression; Moderate deviation from unity; Intercept; Limit theory; Bubble; Economics; Economic Theory
• 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
• Institution: Singapore Management University

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.