Publication Type

Working Paper

Version

publishedVersion

Publication Date

12-2020

Abstract

This paper derives asymptotic properties of the least squares estimator of the autoregressive parameter in local to unity processes with errors being fractional Gaussian noises with the Hurst parameter H. It is shown that the estimator is consistent when H ∈ (0, 1). Moreover, the rate of convergence is n when H ∈ [0.5, 1). The rate of convergence is n2H when H ∈ (0, 0.5). Furthermore, the limit distribution of the centered least squares estimator depends on H. When H = 0.5, the limit distribution is the same as that obtained in Phillips (1987a) for the local to unity model with errors for which the standard functional central theorem is applicable. When H > 0.5 or when H < 0.5, the limit distributions are new to the literature. Simulation studies are performed to check the reliability of the asymptotic approximation for di§erent values of sample size.

Keywords

Least squares, Local to unity, Fractional Brownian motion, Fractional Ornstein-Uhlenbeck process

Discipline

Econometrics

Research Areas

Econometrics

First Page

1

Last Page

17

Publisher

SMU Economics and Statistics Working Paper Series, Paper No. 27-2020

City or Country

Singapore

Download

Included in

Econometrics Commons

Share

COinS