On the maximum of covariance estimators
AbstractLet be a stationary process with mean 0 and finite variances, let [phi]h=E(XkXk+h) be the covariance function and its usual estimator. Under mild weak dependence conditions, the distribution of the vector is known to be asymptotically Gaussian for any , a result having important statistical consequences. Statistical inference requires also determining the asymptotic distribution of the vector for suitable d=dn-->[infinity], but very few results exist in this case. Recently, Wu (2009)  obtained tail estimates for the vector for some sequences dn-->[infinity] and used these to construct simultaneous confidence bands for , 1
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 102 (2011)
Issue (Month): 6 (July)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Harris, David & McCabe, Brendan & Leybourne, Stephen, 2003. "Some Limit Theory For Autocovariances Whose Order Depends On Sample Size," Econometric Theory, Cambridge University Press, vol. 19(05), pages 829-864, October.
- Biao Wu, Wei & Min, Wanli, 2005. "On linear processes with dependent innovations," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 939-958, June.
- Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.
- Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.
- Jirak, Moritz, 2013. "A Darling–Erdös type result for stationary ellipsoids," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1922-1946.
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