Phase and Coherency in a Neighborhood of Zero Frequency for Bivariate Long Memory Series

• Activity Number: 410
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Rebecca J. Sela*+ and Clifford M. Hurvich
• Companies: New York University and New York University
• Keywords: time series ; long memory ; phase ; coherency ; frequency domain ; econometrics

Abstract

The relationship between two long memory time series, as described by the cross-spectral density, is completely described by three terms: the auto-spectral densities, the phase and the coherency. In this paper, we present a general model for bivariate long memory time series that allows for power law behaviors in both the phase and coherency, which had not previously been described in the literature. We prove the consistency of the averaged periodogram estimator for estimating the power law in the coherency. We prove that the narrow band least squares estimator of the cointegrating parameter has a limiting distribution that is not affected by power laws in the phase and coherency, as long as the number of frequencies used in estimation is held fixed. We apply our methods to data on two parts of the money supply and on daily high and low stock prices.