A practical software package for estimating the periodicities in time series by least-squares spectral analysis

Abstract

The researchers investigate some phenomena by continuously observing physical variables, i.e., time series. Nowadays, the Least-Squares Spectral Analysis (LSSA) technique has been preferred for the analysis of time series to conduct more reliable analysis. This technique uses the least-squares principle to estimate the hidden periodicities in the time series. Based on the previous investigations, LSSA gives more reasonable results in the experimental time series that have disturbing effects such as the datum shifts, linear trend, unequally spaced data and etc. The LSSA method is a unique method that can overcome these problems without pre-processing the original series. However, a practical and user-friendly software package in C programming language is not available for scientific purposes to implement the LSSA method. In this paper, we review the computational scheme of the LSSA method, then a software (LSSASOFT) package in the C programming language is developed in the view of the simplicity of the method and compatibility of all types of data. Finally, LSSASOFT is applied in two sample studies for the determining hidden periods in the synthetic data and sea level observations. Consequently, the numerical results indicate that LSSASOFT is a useful tool that can efficiently predicting hidden periodicity for the experimental time series that have disturbing effects.

Keywords

• Least-squares principle
• Periodicity
• Spectral analysis
• Tide-gauge data

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