Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 916731, 8 pages
http://dx.doi.org/10.1155/2013/916731
Research Article

A New Algorithm to Accelerate Harmonic Analysis of Time Series

Department of Applied Mathematics, University of Alicante, P.O. Box 99, 03080 Alicante, Spain

Received 8 November 2012; Accepted 6 December 2012

Academic Editors: H. C. So and H. T. Yau

Copyright © 2013 Pedro A. Martínez-Ortiz and José M. Ferrándiz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.