Slow-explosive AR(1) processes converging to random walk. Issue 9 (2nd May 2020)

• Record Type: Journal Article
• Authors: Kim, Tae Yoon; Hwang, Sun Young
• Is Part Of: Communications in statistics. Volume 49:Issue 9(2020)
• Page Start: 2094
• Page End: 2109
• Publication Date: 2020-05-02
• Subjects: Slow-explosive AR(1) -- U-statistic -- Random Walk; Primary 62M10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1568486
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: This article investigates slow-explosive AR(1) processes, which converge to a random walk (RW) process with logarithm rates, to fill the gap between nearly non-stationary AR(1) and moderately deviated AR(1) processes, and derives the asymptotics of the least squares estimator using central limit theorems for (reduced) U -statistic. We successfully establish the smooth link between the nearly non-stationary AR(1) and the moderately deviated AR(1) processes. Some novel results are reported, which include the convergence of the least squares estimator to a biased fractional Brownian motion.