Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 4, 615--634

Parametric Bootstrap Confidence Intervals for Linear Regression Processes with Long-memory Errors

Mosisa Aga, Auburn University, Montgomery, USA
Tze-Chien Sun, Wayne State University, Detroit, USA

SUMMARY. This paper provides higher-order improvements over the delta method of coverage probability errors of parametric bootstrap confidence intervals (CIs) for the covariance parameters of a time series generated by a regression model with Gaussian stationary long-memory errors. The CIs are based on the plug-in maximum likelihood (PML) estimators. It is shown that, under some sets of conditions on the regression coefficients, the spectral density function and the parameter values, the parametric bootstrap based on the plug-in log-likelihood (PLL) function provides higher-order improvements over the traditional delta method.

AMS (2000) subject classification. Primary 62M10.

Key words and phrases. Confidence interval, delta method, Edgeworth expansion, Gaussian process, linear regression model, long memory process, maximum likelihood estimator, plug-in likelihood function, parametric bootstrap.

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