A Frequency Domain Bootstrap on Whittle Estimation Under Long-Range Dependence

• Activity Number: 623
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Young Min Kim*+ and Dan Nordman
• Companies: Iowa State University and Iowa State University
• Keywords: Fractional ARIMA ; frequency domain bootstrap ; long-range dependence ; M-estimation ; periodogram ; Whittle estimation

Abstract

The frequency domain bootstrap with specified parametric spectral density function under long-range dependence is studied using Whittle likelihood estimation and M-estimation. In contrast to the frequency domain bootstrap under short-range dependence proposed by Dahlhaus and Janas (1996), the parametric spectral density estimates are used instead of the nonparametric spectral density estimates using kernel method because of nonexistent nonparametric spectral density estimators under long-range dependence. This method is valid for a class of broadly used linear long-range dependent processes such as fractional autoregressive integrated moving average processes and fractional Gaussian noise. In some simulation examples, the frequency domain bootstrap has better performance than normal approximation for small sample sizes and the true values for long-memory parameter close to $0$ and $1$, (i.e., at the edges of the parameter space,) when innovation distribution is skewed or heavy-tailed.