Edgeworth Expansion for Linear Regression Processes with Long-Memory Errors

• Published in: Communications in statistics. Theory and methods Vol. 40; no. 4; pp. 663 - 673
• Main Author: Aga, Mosisa
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.01.2011; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Density; Derivatives; Distribution theory; Economic models; Edgeworth expansion; Errors; Exact sciences and technology; Expansion; Gaussian; Gaussian process; General topics; Inference from stochastic processes; time series analysis; Linear inference, regression; Linear regression model; Long memory process; Mathematical models; Mathematics; Maximum likelihood estimator; Plug-in likelihood function; Primary: 62M10; Probability and statistics; Probability theory and stochastic processes; Regression; Regression analysis; Sciences and techniques of general use; Spectra; Spectral density function; Statistics; Time series; Density estimation; Spectral function; Error estimation; Edgeworth expansion; Vector distribution; Linear regression model; Long memory process; Stochastic process; Plug-in likelihood function; Linear model; Maximum likelihood estimator; Log likelihood; Regression function; Distribution function; Stationary process; Primary: 62M10; Likelihood function; Linear regression; Time series; Statistical estimation; Statistical method; Statistical regression; Spectral density function; Regression coefficient; Linear process; Value function; Gaussian process; Regression model; Gaussian processes; Density function; Maximum likelihood; Autocorrelation; Spectral density
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920903447873

This article provides an Edgeworth expansion for the distribution of the log-likelihood derivative LLD of the parameter of a time series generated by a linear regression model with Gaussian, stationary, and long-memory errors. Under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, an Edgeworth expansion of the density as well as the distribution function of a vector of centered and normalized derivatives of the plug-in log-likelihood PLL function of arbitrarily large order is established. This is done by extending the results of Lieberman et al. ( 2003 ), who provided an Edgeworth expansion for the Gaussian stationary long-memory case, to our present model, which is a linear regression process with stationary Gaussian long-memory errors.