A Bootstrap Approach for Nonlinear Autoregressions Some Preliminary Results

Franke, J.; Wendel, Matthias

doi:10.1007/978-3-642-48850-4_13

Cited by 8 publications

(8 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, Efron and Tibshirani [24] proposed to generate bootstrap series by drawing bootstrap innovations independently with replacement from the set of mean adjusted residuals. Generalizations of this approach have been proposed both by Kreiss and Franke [25] to ARMA models and Franke and Wendell [26] to the case of nonlinear autoregressive processes. Applications of this bootstrap method to Markov chains are also available.…”

Section: Bootstrap For Dependent Datamentioning

confidence: 97%

Bootstrap-based ARMA order selection

Fenga

Politis

2011

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

Modelling the underlying stochastic process is one of the main goals in the study of many dynamic phenomena, such as signal processing, system identification and time series. The issue is often addressed within the framework of ARMA (Autoregressive Moving Average) paradigm, so that the related task of identification of the 'true' order is crucial. As it is well known, the effectiveness of such an approach may be seriously compromised by misspecification errors since they may affect model capabilities in capturing dynamic structures of the process. As a result, inference and empirical outcomes may be heavily misleading. Despite the big number of available approaches aimed at determining the order of an ARMA model, the issue is still open. In this paper, we bring the problem in the framework of bootstrap theory in conjunction with the information-based criterion of Akaike (AIC), and a new method for ARMA model selection will be presented. A theoretical justification for the proposed approach as well as an evaluation of its small sample performances, via simulation study, are given.

show abstract

Section: Bootstrap For Dependent Datamentioning

confidence: 97%

Bootstrap-based ARMA order selection

Fenga

Politis

2011

Journal of Statistical Computation and Simulation

View full text Add to dashboard Cite

show abstract

“…(2002a), the bootstrap procedures considered to approximate the distribution of the kernel estimator are the autoregressive bootstrap , the regression bootstrap , and the wild bootstrap . The autoregressive bootstrap follows the proposal of Franke and Wendel (1992) and Kreutzberger (1993). This approach is similar to the residual‐based resampling of linear autoregressions as discussed by Kreiss and Franke (1992).…”

Section: Introductionmentioning

confidence: 99%

Stationary bootstrapping for non-parametric estimator of nonlinear autoregressive model

Hwang

Shin

2010

Journal of Time Series Analysis

View full text Add to dashboard Cite

We consider stationary bootstrap approximation of the non-parametric kernel estimator in a general kth-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.

show abstract

“…The nonparametric autoregressive bootstrap is a generalization of an idea of Efron and Tibshirani (1986) and Holbert and Son (1986) for the case of linear autoregression, and was first proposed by Franke and Wendel (1992) and Kreutzberger (1993). It was proved in Franke et al (2001) that this method is asymptotically consistent for the pointwise distributions of kernel estimators of m. We extend this investigation and derive beyond it some important properties of this bootstrap method; these will allow to apply this autoregressive bootstrap technique also for other problems such as the construction of simultaneous confidence bands and supremum-type tests for the autoregressive function as well as for approximating the distribution of a least squares estimator in a certain parametric model.…”

Section: The Nonparametric Autoregressive Bootstrapmentioning

confidence: 99%

“…For nonparametric estimators of m, autoregressive bootstrap was first proposed by Franke and Wendel (1992) and Kreutzberger (1993). Franke et al (2001) proved consistency of bootstrap for the pointwise distribution of kernel estimates of m and of the conditional variance function.…”

Section: Introductionmentioning

confidence: 99%

Properties of the nonparametric autoregressive bootstrap

Franke

Kreiß

Mammen

et al. 2002

Journal Time Series Analysis

View full text Add to dashboard Cite

For nonparametric autoregression, we investigate a model based bootstrap procedure ('autoregressive bootstrap') that mimics the complete dependence structure of the original time series. We give consistency results for uniform bootstrap confidence bands of the autoregression function based on kernel estimates of the autoregression function. This result is achieved by global strong approximations of the kernel estimates for the resample and for the original sample. Furthermore, it is obtained that the autoregressive bootstrap also yields asymptotically correct approximations for distributions of parametric statistics, for which regression-type bootstrap-techniques like the wild bootstrap do not work. For this purpose, we prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. We propose some particular estimators of the autoregression function and of the density of the innovations such that the mixing coefficients of the autoregressive bootstrap process can be bounded uniformly by some exponentially decaying sequence. This is achieved by using wellestablished coupling techniques. Moreover, by using some 'decoupling' argument, we show that the stationary density of the bootstrap process converges to that of the original process. The paper may serve as a template for proving similar consistency results for other bootstrap techniques such as the Markov bootstrap.

show abstract

A Bootstrap Approach for Nonlinear Autoregressions Some Preliminary Results

Cited by 8 publications

References 4 publications

Bootstrap-based ARMA order selection

Bootstrap-based ARMA order selection

Stationary bootstrapping for non-parametric estimator of nonlinear autoregressive model

Properties of the nonparametric autoregressive bootstrap

Contact Info

Product

Resources

About