The numerical characteristics of repeated least squares spectrum for residual, a newly developed method for time series analysis

Abstract

This paper presents material additional to a previous report on the repeated least squares spectrum for residual method (RLSSR) which was developed for describing long-span variations of the delta-component in sleep electroencephalograms. The RLSSR principally consists of a period-domain calculation based on the application of the least squares spectrum method. The processing allows for unlimited data series length, presents spectrum components with discrete distributions, and provides a good reproduction of the original pattern with the obtained components. These characteristics are quite different from those of the Fourier analysis which is a frequency-domain procedure. The accuracy of the spectrum depends on the ratio of the period between target and full process span. The other numerical characteristics are further clarified using dummy time series patterns. This method is effective to analyze the time series as period-domain spectrum in the biological and also in the other broad fields of science.