Using the Sieve Bootstrap Method in Time Series Analysis

Summary

We consider using bootstrap method for stationary time series problems concerned with prediction intervals for future observations and confidence intervals for the spectral density. Our approach relies on the sieve bootstrap procedure introduced by Bühlmann (1996, 1997) for stationary AR(∞) processes.

We extend the method of obtaining prediction intervals which has been proposed by Stine (1987) for autoregressive time series of known order and compare it with more traditional Gaussian strategy. The introduced sieve-bootstrap approach for constructing confidence intervals for the spectrum is also compared with X ² approximation method and other bootstrap procedure proposed by Pranke and Härdie (1992).

The accuracy of the presented methods is verified via numerical comparison including both Gaussian and non-Gaussian data.