Slow-explosive AR(1) processes converging to random walk

Tae Yoon Kim and Sun Young Hwang

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 9, 2094-2109

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1568486

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