Abstract

We compare and review block, sieve and local bootstraps for time series and thereby illuminate theoretical facts as well as performance on nite-sample data. Our (re-) view is selective with the intention to get a new and fair picture about some particular aspects of bootstrapping time series. The generality of the block bootstrap is contrasted by sieve bootstraps. We discuss implementational dis-/advantages and argue that two types of sieves outperform the block method, each of them in its own important niche, namely linear and categorical processes, respectively. Local bootstraps, designed for nonparametric smoothing problems, are easy to use and implement but exhibit in some cases low performance. Key words and phrases. Autoregression, block bootstrap, categorical time series, context algorithm, double bootstrap, linear process, local bootstrap, Markov chain, sieve bootstrap, stationary process. 1 Introduction Bootstrapping can be viewed as simulating a statistic or statistical pro...

Citations

1998	Bagging predictors - Breiman - 1996
1783	An Introduction to the Bootstrap - Tibshirani, R - 1993
526	Bootstrap methods: another look at the jackknife. Ann Statist - Efron - 1979
442	Time Series: Theory and Methods - Brockwell, Davis - 1991
293	Non-linear Time Series: A Dynamical System Approach - Tong - 1990
286	Time Series: Data Analysis and Theory - Brillinger - 1981
275	Bootstrap methods and their application - Davison - 1997
162	The jackknife and the bootstrap for general stationary observations - Künsch - 1989
159	The Statistical Analysis of Time Series - Anderson - 1971
139	Multiple Time Series - Hannan - 1970
119	Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy - EFRON, TIBSHIRANI - 1986
119	Abstract Inference - Grenander - 1981
118	Some asymptotic theory for the bootstrap - Bickel, Freedman - 1981
116	The Stationary Bootstrap - Politis, Romano - 1994
114	B: Model selection and the principle of minimum description length - MH, Yu
85	Time series analysis and its applications - Shumway, Stoffer - 2005
84	Fitting time series models to nonstationary processes - Dahlhaus - 1997
67	Time Series: Theory and Methods. Second edition - Brockwell, Davies - 1991
66	Variable length markov chains - Buhlmann, Wyner - 1999
60	Nonparametric Maximum Likelihood Estimation by the Method of Sieves,” Annals of Statistics - Geman, Hwang - 1982
57	The fourier integral and certain of its applications - Wiener - 1967
52	Consistent autoregressive spectral estimates - Berk - 1974
52	Moving blocks jackknife and bootstrap capture weak dependence - Liu, Singh - 1992
48	Statistical Methods for Forecasting - Abraham, Ledolter
47	The use of subseries values for estimating the variance of a general statistic from a stationary sequence - Carlstein - 1986
45	On Blocking Rules for the Bootstrap with Dependent Data - HALL, HOROWITZ, et al. - 1992
35	Elements of Multivariate Time Series Analysis (2nd ed - Reinsel - 2003
33	Edgeworth correction by bootstrap in autoregressions - Bose - 1988
25	Robust Statistics: The Approach Based on In Functions - Hampel, Ronchetti, et al. - 1986
21	On bootstrapping kernel spectral estimates - Franke, Härdle - 1992
20	On bootstrapping two-stage least-squares estimates in stationary linear models - Freedman - 1984
20	A General Resampling Scheme for Triangular Arrays of αmixing Random Variables with Application to the Problem of Spectral Density Estimation - Politis, Romano - 1992
19	On Consistent Estimates of the Spectrum of a Stationary Time Series - Parzen - 1957
18	Resampling a coverage pattern - HALL - 1985
16	Moment bounds for stationary mixing sequences - Yokoyama - 1980
16	Bootstrap of kernel smoothing in nonlinear time series - Franke, Kreiss, et al. - 2002
16	Some automated methods of smoothing time-dependent data - Hart - 1996
15	Robust Statistics: The Approach based on In uence Functions - Hampel, Ronchetti, et al. - 1986
15	Second-order Correctness of the Blockwise Bootstrap for Stationary Observations - GÖTZE, KÜNSCH - 1996
14	Blockwise bootstrapped empirical process for stationary sequences.Ann - Bühlmann - 1994
14	Approximation Theorems of Mathematical Statistics - ing, J - 1980
14	Model checking via parametric bootstraps in time series analysis - Tsay - 1992
11	Bootstrapping stationary autoregressive moving-average models - Kreiss, Franke - 1992
11	Validity of blockwise bootstrap for empirical process with stationary observations - Naik-Ninbalkar, Rajarshi - 1994
11	On Studentizing and Blocking Methods for Implementing the Bootstrap with Dependent Data - Davison, Hall - 1993
10	Block length selection in the bootstrap for time series. Research Report 72, Seminar für Statistik - Bühlman, Künsch - 1994
10	Rational Transfer Function Approximation - Hannan - 1987
10	A new mixing notion and functional central limit theorems for a sieve bootstrap in time series - Bickel, Bühlmann - 1999
10	Model selection for variable length Markov chains and tuning the context algorithm - Bühlmann
10	A frequency domain bootstrap for ratio statistics in time series analysis - Dahlhaus, Janas - 1996