Large-sample inference for nonparametric regression with dependent errors
AbstractA central limit theorem is given for certain weighted partial sums of a covariance stationary process, assuming it is linear in martingale differences, but without any restriction on its spectrum. We apply the result to kernel nonparametric fixed-design regression, giving a single central limit theorem which indicates how error spectral behavior at only zero frequency influences the asymptotic distribution and covers long-range, short-range and negative dependence. We show how the regression estimates can be Studentized in the absence of previous knowledge of which form of dependence pertains, and show also that a simpler Studentization is possible when long-range dependence can be taken for granted.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by London School of Economics and Political Science in its series Open Access publications from London School of Economics and Political Science with number http://eprints.lse.ac.uk/302/.
Date of creation: 1997
Date of revision:
Publication status: Published in Annals of statistics (1997) v.25, p.2054-2083
Contact details of provider:
Web page: http://www.lse.ac.uk
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Deo, R. S., 1997. "Nonparametric regression with long-memory errors," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 89-94, April.
- Robinson, P M, 1993. "Highly Insignificant F-Ratios," Econometrica, Econometric Society, vol. 61(3), pages 687-96, May.
- Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
- Adam McCloskey, 2012.
"Estimation of the Long-Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends,"
2012-17, Brown University, Department of Economics.
- Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, 05.
- Jianqing Fan & Yingying Fan & Jinchi Lv, 0. "Aggregation of Nonparametric Estimators for Volatility Matrix," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(3), pages 321-357.
- Morten Ørregaard Nielsen & Per Frederiksen, 2008. "Fully Modified Narrow-Band Least Squares Estimation of Stationary Fractional Cointegration," Working Papers 1171, Queen's University, Department of Economics.
- Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
- Andrew Jeffrey, 2004. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 251-289.
- Dedecker, Jérôme & Merlevède, Florence, 2011. "Rates of convergence in the central limit theorem for linear statistics of martingale differences," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1013-1043, May.
- Karlsen, Hans Arnfinn & Tjostheim, Dag, 1998. "Nonparametric estimation in null recurrent times series," SFB 373 Discussion Papers 1998,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Youndjé, É. & Vieu, P., 2006. "A note on quantile estimation for long-range dependent stochastic processes," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 109-116, January.
- Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, .
"Residual Log-Periodogram Inference for Long-Run-Relationships,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/4431, Universidad Carlos III de Madrid.
- Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
- Hassler, Uwe & Marmol, Francesc & Velasco, Carlos, 2002. "Residual Log-Periodogram Inference for Long-Run-Relationships," Darmstadt Discussion Papers in Economics 37317, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute of Economics (VWL).
- Hassler, U. & Marmol, Francesc & Velasco, Carlos, . "Residual log-periodogram inference for long-run relationships," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4359, Universidad Carlos III de Madrid.
- Adam McCloskey & Pierre Perron, 2012.
"Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends,"
2012-15, Brown University, Department of Economics.
- Pierre Perron & Adam McCloskey, 2010. "Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends," Boston University - Department of Economics - Working Papers Series WP2010-048, Boston University - Department of Economics.
- Robinson, Peter M., 2012. "Nonparametric trending regression with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 4-14.
- Gao, jiti & Anh, vo & Heyde, christopher, 1999.
"Statistical estimation of nonstationaryGaussian processes with long-range dependence and intermittency,"
11972, University Library of Munich, Germany, revised 23 Oct 2001.
- Gao, Jiti & Anh, Vo & Heyde, Chris, 2002. "Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 295-321, June.
- repec:dar:vpaper:37317 is not listed on IDEAS
- Hidalgo, J., 2008. "Specification testing for regression models with dependent data," Journal of Econometrics, Elsevier, vol. 143(1), pages 143-165, March.
- Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (LSE Research Online).
If references are entirely missing, you can add them using this form.