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The multivariate linear process bootstrap
Jentsch, Carsten
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Politis, Dimitris N.
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URL:
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http://mammen.vwl.uni-mannheim.de/fileadmin/user_u...
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Document Type:
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Conference or workshop publication
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Year of publication:
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2011
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Book title:
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Proceedings of the 17th European Young Statisticians Meeting, EYSM, 5-9 September 2011, Lisbon, Portugal
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Page range:
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1-4
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Conference title:
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17th European Young Statisticians Meeting
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Location of the conference venue:
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Lisbon, Portugal
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Date of the conference:
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5.-9. September 2011
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Place of publication:
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Lisboa
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Publishing house:
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Univ. Nova de Lisboa. Faculdade de Ciências e Tecnologia
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Publication language:
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English
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Institution:
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School of Law and Economics > Statistik (Mammen)
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Subject:
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510 Mathematics
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Classification:
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Keywords (English):
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Banded covariance matrix estimator , bootstrap , linear pro cess , multivariate time series
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Abstract:
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The linear process bootstrap (LPB) for univariate time seri
es has been introduced by McMurry
and Politis (2010) and it is called LPB because it generates l
inear processes in the bootstrap domain.
However, it does not assume that the data are themselves a sam
ple from a linear process. They use
tapered and banded estimates for the autocovariance matrix
of the whole data stretch [cf. Wu and
Pourahmadi (2009)] and i.i.d. resampling of appropriately
standardized residuals. Under a physical
dependence assumption [cf. Wu (2005)], they show validity o
f the LPB for the sample mean.
In this paper, we generalize their approach to the case of mul
tivariate time series and show its
validity for the sample mean under different assumptions (mi
xing, weak dependence, linearity). To
complement the theory of McMurry and Politis (2010), we show
that the multivariate LPB works
also for spectral density estimation, but that it fails gene
rally for sample autocovariances. Even in
the univariate case and under assumed linearity, this is sti
ll the case. However, we show consistency
of the LPB for univariate, causal and invertible linear processes for higher order statistics as e.g. autocovariances and for autocorrelations in the univariate case under linearity only. Moreover, the validity of the LPB for the multivariate sample mean can be used in order to correct the invalidity of the univariate LPB for higher order statistics as e.g. autocovariances in the general case. For this purpose, an LPB-of-blocks bootstrap scheme is proposed.
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 | Dieser Eintrag ist Teil der Universitätsbibliographie. |
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