Detecting Hidden 'Peaks' in ARMA Spectral Estimators

• Activity Number: 406
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Wayne Woodward*+ and Henry L Gray and Alan C Elliott
• Companies: Southern Methodist University and Southern Methodist University and The University of Texas Southwestern Medical Center at Dallas
• Keywords: frequency ; spectrum ; autoregressive model ; factor table ; stationary process

Abstract

Autoregressive (AR) and autoregressive moving-average (ARMA) spectral estimators have been shown to be useful for providing model-based estimates of the spectrum of a stationary process. The standard procedure for implementing such an estimator is to fit an AR or ARMA model to the data using model identification procedures such as AIC and finding the maximum likelihood estimates of the model parameters. The corresponding AR or ARMA spectral density estimate is a plot of the true spectral density for the fitted model, and it often provides relatively smooth spectral densities with good peak detection capabilities. Often, however, certain weaker frequencies that are actually in the data and are important to the analysis are not manifested by a peak in the spectrum. We discuss the use of the factor table (see Woodward, Gray, and Elliott, 2012) for obtaining underlying frequency information in an AR or ARMA spectral estimator that is not expressed by actual peaks in the spectrum.