Mild-explosive and local-to-mild-explosive autoregressions with serially correlated errors

• Main Authors: LUI, Yiu Lim, XIAO, Weilin, YU, Jun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Anti-persistent; Unit root; Mildly explosive; Limit theory; Bubble; Fractional integration; Young integral; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2222; https://ink.library.smu.edu.sg/context/soe_research/article/3221/viewcontent/Antipersistence15_.pdf
• Institution: Singapore Management University

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.