The multiple hybrid bootstrap - Resampling multivariate linear processes

DOI:	https://doi.org/10.1016/j.jmva.2010.06.005
URL:	https://www.sciencedirect.com/science/article/pii/...
Weitere URL:	http://nber-nsf09.ucdavis.edu/program/papers/jents...
Dokumenttyp:	Zeitschriftenartikel
Erscheinungsjahr:	2010
Titel einer Zeitschrift oder einer Reihe:	Journal of Multivariate Analysis : JMVA
Band/Volume:	101
Heft/Issue:	10
Seitenbereich:	2320-2345
Ort der Veröffentlichung:	Amsterdam [u.a.]
Verlag:	Elsevier
ISSN:	0047-259X , 1095-7243
Verwandte URLs:	https://www.statistik.tu-dortmund.de/fil...
Sprache der Veröffentlichung:	Englisch
Einrichtung:	Fakultät für Rechtswissenschaft und Volkswirtschaftslehre > Statistik (Mammen)
Fachgebiet:	510 Mathematik
Fachklassifikation:	MSC: 62G09 ; 62M10 ; 62H12,
Freie Schlagwörter (Englisch):	Frequency domain bootstrap ; Multivariate bootstrap ; Multivariate linear time series ; Kernel estimators ; Discrete Fourier transform ; Cholesky decomposition ; Spectral density matrix ; Autocovariance matrix ; Sample mean
Abstract:	The paper reconsiders the autoregressive aided periodogram bootstrap (AAPB) which has been suggested in Kreiss and Paparoditis (2003) [18]. Their idea was to combine a time domain parametric and a frequency domain nonparametric bootstrap to mimic not only a part but as much as possible the complete covariance structure of the underlying time series. We extend the AAPB in two directions. Our procedure explicitly leads to bootstrap observations in the time domain and it is applicable to multivariate linear processes, but agrees exactly with the AAPB in the univariate case, when applied to functionals of the periodogram. The asymptotic theory developed shows validity of the multiple hybrid bootstrap procedure for the sample mean, kernel spectral density estimates and, with less generality, for autocovariances.