A Simple Bootstrap Method for Time Series

In this article we present a simple bootstrap method for time series. The proposed method is model-free, and hence it enables us to avoid certain situations where the bootstrap samples may contain impossible values due to resampling from the residuals. The method is easy to implement and can be applied to stationary and nonstationary time series. The simulation results and the application to real time series data show that the method works very well.

[1]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[2]  Yun B. Kim,et al.  Simulation output analysis using the threshold bootstrap , 2001, Eur. J. Oper. Res..

[3]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[4]  Regina Y. Liu Bootstrap Procedures under some Non-I.I.D. Models , 1988 .

[5]  P. Bühlmann Bootstraps for Time Series , 2002 .

[6]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[7]  Wolfgang Härdle,et al.  On Bootstrapping Kernel Spectral Estimates , 1992 .

[8]  T. Willemain,et al.  The threshold bootstrap and threshold jackknife , 1999 .

[9]  B. Efron The jackknife, the bootstrap, and other resampling plans , 1987 .

[10]  Regina Y. Liu Moving blocks jackknife and bootstrap capture weak dependence , 1992 .

[11]  J. Swanepoel,et al.  The bootstrap applied to power spectral density function estimation , 1986 .

[12]  H. Künsch The Jackknife and the Bootstrap for General Stationary Observations , 1989 .

[13]  J. Fox Bootstrapping Regression Models , 2002 .

[14]  Jorge Haddock,et al.  The binary bootstrap: inference with autocorrelated binary data , 1993 .

[15]  W. Härdle,et al.  Bootstrapping in Nonparametric Regression: Local Adaptive Smoothing and Confidence Bands , 1988 .

[16]  Joseph P. Romano,et al.  A General Resampling Scheme for Triangular Arrays of $\alpha$-Mixing Random Variables with Application to the Problem of Spectral Density Estimation , 1992 .