A Method for Determining Periods in Time Series

Abstract

The periods corresponding to peaks in the autoregressive and window spectral density estimators are shown to be consistent and asymptotically normal estimators of peak periods in the true spectral density under assumptions of known autoregressive order and under slight modifications of the assumptions often made to show the asymptotic normality of window estimators, respectively. The asymptotic variances are obtained, and the use of the theory is illustrated by obtaining an asymptotic confidence interval for a peak period using a set of hormone data.

Key Words:

• Spectral density function
• Autoregressive spectral estimator
• Window spectral estimator