Abstract
In this paper we will deal with an application of Efron’s 1979 bootstrap to stationary stochastic processes in discrete time. In many applications it is assumed that these processes are of autoregressive or more generally of autoregressive moving average type, i.e. the underlying stationary process X = (X t: t ∈ Z = {0, ±1, ±2,…}) is assumed to satisfy the following stochastic difference equation
Here ε = (ε t: t ∈ Z) denotes a white noise, that is a sequence of uncorrelated, zero mean random variables with finite variance σ 2.
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References
Bickel, P.J. and Freedman, D.A. (1981). Some Asymptotic theory for the bootstrap. Ann. Statist 9, 1196–1217.
Bose, A. (1988). Edgeworth corrections by bootstrap in autoregressions. Ann. Statist. 16, 1709–1722.
Brown, B.M. (1971). Martingale central limit theorems. Ann. Math. Statist. 42, 54–66.
Efron, B. and Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Science 1, 54–77.
Franke, J. and Kreiss, J.-P. (1989). Bootstrapping stationary ARMA models. Preprint Submitted.
Freedman, D.A. (1984). On bootstrapping two-stage least-squares estimates in stationary linear models. Ann. Statist. 12, 827–842.
Kreiss, J.-P. (1988). Asymptotic statistical inference for a class of stochastic processes. Habilitationsschrift. University of Hamburg.
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© 1992 Springer-Verlag Berlin Heidelberg
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Kreiss, JP. (1992). Bootstrap procedures for AR (∞) — processes. In: Jöckel, KH., Rothe, G., Sendler, W. (eds) Bootstrapping and Related Techniques. Lecture Notes in Economics and Mathematical Systems, vol 376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48850-4_14
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DOI: https://doi.org/10.1007/978-3-642-48850-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55003-7
Online ISBN: 978-3-642-48850-4
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