Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Definition of Long Memory Read chapter Read first chapter

2013 | OriginalPaper | Chapter

10. Resampling

Authors : Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik

Published in: Long-Memory Processes

Publisher: Springer Berlin Heidelberg

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Resampling or bootstrap methods refer to techniques where statistical inference is based on a simulated distribution of a statistic T n obtained by resampling from an observed sample X 1,…,X n . Inference of this type is always conditional on the sample. In the most general version, no model assumptions are used except for global conditions such as stationarity, existence of some moments, etc. In the most restricted version, a parametric model is specified and resampling is used only as a simple way of obtaining an approximate distribution of T n . Note that different terms such as ‘bootstrap’, ‘resampling’, ‘subsampling’, etc. are used in the literature for different variations of the same general idea. Since there does not seem to be a unified terminology, we use ‘resampling’ and ‘bootstrap’ as synonyms.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Spatial and Space-Time Processes
Literature
Andrews, D., & Lieberman, O. (2005). Valid Edgeworth expansions for the Whittle maximum likelihood estimator for stationary long-memory Gaussian time series. Econometric Theory, 21, 710–734. MathSciNetMATHCrossRef
Andrews, W. K., Lieberman, O., & Marmer, V. (2006). Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes. Journal of Econometrics, 133, 673–702. MathSciNetCrossRef
Beran, J., & Shumeyko, Y. (2012a). On asymptotically optimal wavelet estimation of trend functions under long-range dependence. Bernoulli, 189(1), 137–176. MathSciNetCrossRef
Beran, J., & Shumeyko, Y. (2012b). Bootstrap testing for discontinuities under long-range dependence. Journal of Multivariate Analysis, 105(1), 322–347. MathSciNetMATHCrossRef
Bhansali, R. J., Giraitis, L., & Kokoszka, P. S. (2006). Estimation of the memory parameter by fitting fractionally differenced autoregressive models. Journal of Multivariate Analysis, 97(10), 2101–2130. MathSciNetMATHCrossRef
Carlstein, E. (1986). The use of subseries methods for estimating the variance of a general statistic from a stationary time series. The Annals of Statistics, 14, 1171–1179. MathSciNetMATHCrossRef
Choi, E., & Hall, P. G. (2000). Bootstrap confidence regions from autoregressions of arbitrary order. Journal of the Royal Statistical Society B, 62, 461–477. MathSciNetMATHCrossRef
Faÿ, G., Moulines, E., & Soulier, P. (2004). Edgeworth expansions for linear statistics of possibly long range dependent linear processes. Statistics & Probability Letters, 66(3), 275–288. MathSciNetMATHCrossRef
Giraitis, L., & Robinson, P. M. (2003). Edgeworth expansions for semiparametric Whittle estimation of long memory. The Annals of Statistics, 31(4), 1325–1375. MathSciNetCrossRef
Hall, P. (1992). The bootstrap and Edgeworth expansion. New York: Springer.
Hall, P., Jing, B.-Y., & Lahiri, S. N. (1998). On the sampling window method for long-range dependent data. Statistica Sinica, 8, 1189–1204. MathSciNetMATH
Hannan, E. J., & Deistler, M. (1988). The statistical theory of linear systems. New York: Wiley. MATH
Jach, A., McElroy, T., & Politis, D. N. (2012). Subsampling inference for the mean of heavy-tailed long memory time series. Journal of Time Series Analysis, 33, 96–111. MathSciNetCrossRef
Kim, Y. M., & Nordman, D. J. (2011) Properties of a block bootstrap under long-range dependence. Sankhya A, 73(1), 79–109. MathSciNetCrossRef
Künsch, H. R. (1989). The jackknife and bootstrap for general stationary observations. The Annals of Statistics, 17, 1217–1261. MathSciNetMATHCrossRef
Lieberman, O., & Phillips, P. C. B. (2004). Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter. Econometric Theory, 20, 464–484. MathSciNetMATHCrossRef
Lieberman, O., Rousseau, J., & Zucker, D. M. (2001). Valid Edgeworth expansion for the sample autocorrelation function under long range dependence. Econometric Theory, 17, 257–275. MathSciNetMATHCrossRef
Lieberman, O., Rousseau, J., & Zucker, D. (2003). Valid asymptotic expansions for the maximum likelihood estimator of the parameter of a stationary, Gaussian, strongly dependent process. The Annals of Statistics, 31(2), 586–612. MathSciNetMATHCrossRef
McElroy, T., & Politis, D. N. (2007). Self-normalization for heavy-tailed time series with long memory. Statistica Sinica, 17(1), 199–220. MathSciNetMATH
Nordman, D. J., & Lahiri, S. N. (2005). Validity of the sampling window method for long-range dependent linear processes. Econometric Theory, 21, 1087–1111. MathSciNetMATHCrossRef
Nordman, D. J., Sibbertsen, P., & Lahiri, S. N. (2006). Empirical likelihood confidence intervals for the mean of a long-range dependence process. Journal of Time Series Analysis, 28(4), 576–599. MathSciNetCrossRef
Parzen, E. (1974). Some recent advances in time series modeling. IEEE Transactions on Automatic Control, AC-19, 723–730. MathSciNetCrossRef
Politis, D. N., & Romano, J. P. (1993). Nonparametric resampling for homogeneous strong mixing random fields. Journal of Multivariate Analysis, 47(2), 301–328. MathSciNetMATHCrossRef
Poskitt, D. S. (2007a). Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases. Annals of the Institute of Statistical Mathematics, 59(4), 697–725. MathSciNetMATHCrossRef
Poskitt, D. S. (2007b). Properties of the sieve bootstrap for fractionally integrated and non-invertible processes. Journal of Time Series Analysis, 29(2), 224–250. MathSciNetCrossRef
Shibata, R. (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. The Annals of Statistics, 8, 147–164. MathSciNetMATHCrossRef
Metadata
Title
Resampling
Authors
Jan Beran
Yuanhua Feng
Sucharita Ghosh
Rafal Kulik
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Long-Memory Processes

Print ISBN: 978-3-642-35511-0

Electronic ISBN: 978-3-642-35512-7

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-35512-7_10

Premium Partner

    Image Credits