The Annals of Statistics

A frequency domain empirical likelihood for short- and long-range dependence

Daniel J. Nordman and Soumendra N. Lahiri

Full-text: Open access

Abstract

This paper introduces a version of empirical likelihood based on the periodogram and spectral estimating equations. This formulation handles dependent data through a data transformation (i.e., a Fourier transform) and is developed in terms of the spectral distribution rather than a time domain probability distribution. The asymptotic properties of frequency domain empirical likelihood are studied for linear time processes exhibiting both short- and long-range dependence. The method results in likelihood ratios which can be used to build nonparametric, asymptotically correct confidence regions for a class of normalized (or ratio) spectral parameters, including autocorrelations. Maximum empirical likelihood estimators are possible, as well as tests of spectral moment conditions. The methodology can be applied to several inference problems such as Whittle estimation and goodness-of-fit testing.

Article information

Source
Ann. Statist., Volume 34, Number 6 (2006), 3019-3050.

Dates
First available in Project Euclid: 23 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1179935073

Digital Object Identifier
doi:10.1214/009053606000000902

Mathematical Reviews number (MathSciNet)
MR2329476

Zentralblatt MATH identifier
1114.62095

Subjects
Primary: 62F40: Bootstrap, jackknife and other resampling methods 62G09: Resampling methods
Secondary: 62G20: Asymptotic properties

Keywords
Empirical likelihood estimating equations long-range dependence periodogram spectral distribution Whittle estimation

Citation

Nordman, Daniel J.; Lahiri, Soumendra N. A frequency domain empirical likelihood for short- and long-range dependence. Ann. Statist. 34 (2006), no. 6, 3019--3050. doi:10.1214/009053606000000902. https://projecteuclid.org/euclid.aos/1179935073


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