Accession Number : ADA132466

Title :   The Amplitude Density Function and High-Resolution Frequency Analysis of Time Series.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CA DEPT OF STATISTICS

Personal Author(s) : Izenman,Alan Julian

PDF Url : ADA132466

Report Date : 06 Sep 1983

Pagination or Media Count : 67

Abstract : This paper describes the amplitude density function which is used to screen, identify and resolve frequencies in a time series. The technique is derived from the spectral representation of the sum of an harmonic regression function and a stochastic error process, and on the inversion theorem associated with that representation. The amplitude density function possesses the desirable properties of statistical consistency and high frequency resolution, and is related to the Fourier transform of a finite-length time series. Following the identification by the amplitude density function of the dominant frequencies in a time series, regression methods are used to fit a hidden periodicities model to the data. Also introduced is in a high-resolution frequency trace to investigate the extent and direction of nonstationarity in a time series. These techniques are illustrated with a detailed frequency analysis of the annual sunspot numbers series from 1749 to 1979, and includes analysis of a physically motivated data transformation of the sunspot series.

Descriptors :   *Time series analysis, *Frequency, Amplitude, Density, Functions, High frequency, High resolution, Fourier transformation, Spectra, Harmonics, Regression analysis, Inversion, Theorems, Stochastic processes, Errors, Sunspots

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE