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Stationary bootstrapping for non‐parametric estimator of nonlinear autoregressive model
Author(s) -
Hwang Eunju,
Shin Dong Wan
Publication year - 2011
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00699.x
Subject(s) - autoregressive model , mathematics , bootstrapping (finance) , estimator , star model , kernel (algebra) , nonlinear autoregressive exogenous model , setar , parametric statistics , stationary ergodic process , kernel density estimation , statistics , ergodic theory , econometrics , autoregressive integrated moving average , time series , mathematical analysis , combinatorics , invariant measure
We consider stationary bootstrap approximation of the non‐parametric kernel estimator in a general k th‐order nonlinear autoregressive model under the conditions ensuring that the nonlinear autoregressive process is a geometrically Harris ergodic stationary Markov process. We show that the stationary bootstrap procedure properly estimates the distribution of the non‐parametric kernel estimator. A simulation study is provided to illustrate the theory and to construct confidence intervals, which compares the proposed method favorably with some other bootstrap methods.