Prediction Intervals for the Local Spectrum Estimate

• Activity Number: 412
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Kara Stevens*+ and Guy Nason
• Companies: University of Bristol and University of Bristol
• Keywords: Locally stationary process ; local spectrum predication intervals ; Bayesian wavelet shrinkage

Abstract

For locally stationary processes with slowly evolving second order structures it can often be important to produce an accurate estimate of the localized autocovariance (LACV). In locally stationary wavelet (LSW) models the LACV can be estimated via the evolutionary wavelet spectrum (EWS). Estimates of the EWS from wavelet periodograms are asymptotically unbiased but not consistent. We discuss techniques to improve the estimate of the EWS of a LSW process. Our method attempts to 'denoise' the wavelet periodograms via variance stabilisation and Bayesian wavelet shrinkage. Our method has the advantage of being able to obtain predication intervals and probabilities associated with the EWS estimates. These could be used to select an appropriate wavelet basis. We demonstrate our method's performance assuming independence between scales and compare it to standard methods.