The local bootstrap for Markov processes

A nonparametric bootstrap procedure is proposed for stochastic processes which follow a general autoregressive structure. The procedure generates bootstrap replicates by locally resampling the original set of observations reproducing automatically its dependence properties. It avoids an initial nonp...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2002-11, Vol.108 (1), p.301-328
Main Authors: Paparoditis, Efstathios, Politis, Dimitris N.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Inference from stochastic processes
time series analysis
Markov dependence
Mathematics
Nonlinear time series
Nonparametric inference
Probability and statistics
Resampling
Sciences and techniques of general use
Statistics
Time reversibility
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Summary:A nonparametric bootstrap procedure is proposed for stochastic processes which follow a general autoregressive structure. The procedure generates bootstrap replicates by locally resampling the original set of observations reproducing automatically its dependence properties. It avoids an initial nonparametric estimation of process characteristics in order to generate the pseudo-time series and the bootstrap replicates mimic several of the properties of the original process. Applications of the procedure in nonlinear time-series analysis are considered and theoretically justified; some simulated and real data examples are discussed.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(02)00315-4