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

By Daniel J. Nordman, Soumendra Nath Lahiri. 2007

76 citations recorded by the source corpus.

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.

Subfields: Control and Systems Engineering, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5268b80c8461ab19a1f743fb70a6499465053f81

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Peter M. Robinson
2. Y. Kitamura

In Finance

1. J. Hualde
2. Peter M. Robinson
3. Morten Ørregaard Nielsen
4. Y. Kitamura
5. Katsumi Shimotsu
6. Søren Johansen
7. Ngai Hang Chan
8. Boris Buchmann

In Statistics and Probability

1. J. Hualde
2. Peter M. Robinson
3. Y. Kitamura
4. Morten Ørregaard Nielsen
5. Xiaohong Chen
6. Liangjun Su
7. Stefan Wager
8. G. Frazer

Citations in the corpus

• Empirical Likelihood Methods in Econometrics: Theory and Practice (2006, background): “Schennach (2004) and Ragusa (2005) present interesting higher-order asymptotic results that are closely related to those of Newey and Smith (2004).”
• A self‐normalized approach to confidence interval construction in time series (2010, unknown): “nce has been given. Other works that avoid direct estimation include Dahlhaus and Janas (1996) and Kreiss and Paparoditis (2003) on the frequency domain bootstrap method (Franke and H¨ardle 1992) and Nordman and Lahiri (2006) on the empirical-likelihoodbased approach. A limitation of these works is ”
• Gaussian pseudo-maximum likelihood estimation of fractional time series models (2011, background): “More recently, [16] considered empirical maximum likelihood inference covering this setting.”