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

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 06, 1983
Accession Number
ADA132466

Entities

People

  • Alan Julian Izenman

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programs
  • Data Mining
  • Data Science
  • Estimators
  • Frequency
  • Frequency Bands
  • High Resolution
  • Information Science
  • New York
  • Power Spectra
  • Probability
  • Random Variables
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Stochastic Processes

Readers

  • Approximation Theory.
  • Image Processing and Computer Vision.
  • Statistical inference.