Unit Root Log Periodogram Regression

• Main Author: PHILLIPS, Peter C. B.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2007
• Subjects: Asymptotic independence; Discrete Fourier transform; Fractional integration; Log periodogram regression; Long memory parameter; Nonstationarity; Semiparametric estimation; Unit root; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/283; https://ink.library.smu.edu.sg/context/soe_research/article/1282/viewcontent/Unit_Root_Log_Periodogram_2007.pdf
• Institution: Singapore Management University

Log periodogram (LP) regression is shown to be consistent and to have a mixed normal limit distribution when the memory parameter d=1. Gaussian errors are not required. The proof relies on a new result showing that asymptotically infinite collections of discrete Fourier transforms (dft's) of a short memory process at the fundamental frequencies in the vicinity of the origin can be treated as asymptotically independent normal variates, provided one does not include too many dft's in the collection.