## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 8, Number 1 (2014), 1460-1490.

### On the Bartlett correction of empirical likelihood for Gaussian long-memory time series

Ngai Hang Chan, Kun Chen, and Chun Yip Yau

#### Abstract

Bartlett correction is one of the desirable features of empirical likelihood (EL) since it allows constructions of confidence regions with improved coverage probabilities. Previous studies demonstrated the Bartlett correction of EL for independent observations and for short-memory time series. By establishing the validity of Edgeworth expansion for the signed root empirical log-likelihood ratio, the validity of Bartlett correction of EL for Gaussian long-memory time series is established. In particular, orders of the coverage error of confidence regions can be reduced from $\log^{6}n/n$ to $\log^{3}n/n$, which is different from the classical rate of reduction from $n^{-1}$ to $n^{-2}$.

#### Article information

**Source**

Electron. J. Statist., Volume 8, Number 1 (2014), 1460-1490.

**Dates**

First available in Project Euclid: 26 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1409058255

**Digital Object Identifier**

doi:10.1214/14-EJS930

**Mathematical Reviews number (MathSciNet)**

MR3545163

**Zentralblatt MATH identifier**

1298.62037

**Subjects**

Primary: 62F10: Point estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

**Keywords**

Coverage error Edgeworth expansion periodogram Whittle likelihood

#### Citation

Chan, Ngai Hang; Chen, Kun; Yau, Chun Yip. On the Bartlett correction of empirical likelihood for Gaussian long-memory time series. Electron. J. Statist. 8 (2014), no. 1, 1460--1490. doi:10.1214/14-EJS930. https://projecteuclid.org/euclid.ejs/1409058255