Bootstrap confidence bands for spectra and cross-spectra

A nonparametric method for setting confidence intervals and confidence bands for spectra and cross-spectra of stationary weakly dependent time series is presented. The proposed methodology involves using a bootstrap resampling scheme that was recently developed for use in time series problems. A computing algorithm is provided, along with guidelines on its practical application. Finally, results of simulations with artificially generated data are shown as an illustration of the method's potential. >

[1]  M. Bartlett.  On the Theoretical Specification and Sampling Properties of Autocorrelated Time‐Series , 1946 .

[2]  M. Bartlett.  Periodogram analysis and continuous spectra. , 1950, Biometrika.

[3]  John W. Van Ness,et al.  The Maximum Deviation of Sample Spectral Densities , 1967 .

[4]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[5]  Y. Katznelson.  An Introduction to Harmonic Analysis: Interpolation of Linear Operators , 1968 .

[6]  E. J. Hannan,et al.  Multiple time series , 1970 .

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

[8]  I. G. Zhurbenko,et al.  A limit theorem for spectral density statistics with time shift , 1980 .

[9]  K. Singh,et al.  On the Asymptotic Accuracy of Efron's Bootstrap , 1981 .

[10]  David R. Brillinger,et al.  Time Series: Data Analysis and Theory. , 1982 .

[11]  D. Thomson,et al.  Spectrum estimation and harmonic analysis , 1982, Proceedings of the IEEE.

[12]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

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

[14]  Soumendra N. Lahiri,et al.  Second order optimality of stationary bootstrap , 1991 .

[15]  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 .