Publication Type

Journal Article

Version

acceptedVersion

Publication Date

4-2023

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 2 (0; 1). It is shown that the estimator is consistent for all values of H 2 (0; 1). Moreover, the rate of convergence is n 1 when H 2 [0:5; 1). The rate of convergence is n 2H when H 2 (0; 0:5). Furthermore, the limiting distribution of the centered least squares estimator depends on H. When H = 0:5, the limiting distribution is the same as that obtained in Phillips (1987a) for the local to unity model with errors for which the standard functional central limit theorem is applicable. When H > 0:5 or when H

Keywords

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

Discipline

Econometrics

Research Areas

Econometrics

Publication

Advances in Econometrics

Volume

45A

First Page

73

Last Page

95

ISSN

0731-9053

Identifier

10.1108/S0731-90532023000045A002

Publisher

Jai Press Inc.

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1108/S0731-90532023000045A002

Included in

Econometrics Commons

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