A novel method of time series analysis, and an application to the study of human sleep electroencephalogram

Abstract

A new mathematical method was developed to analyze time series. Applications of this method to the delta component of all-night sleep electroencephalogram (EEG) revealed new variations with double-rapid eye movement (REM)-sleep interval. The proposed method entails repeated application of the least squares spectrum. First, the conventional least squares spectrum calculation is applied to the time series. Using the parameters of the peak components in the obtained spectrum, an intermediate time series is reconstructed. The residual time series is made by subtracting the intermediate time series from the previous time series. Next, the least squares calculation is again applied to the residual time series. These procedures are repeated until the component cannot be detected. We named this new method the Repeated Least Squares Spectrum for the Residual (RLSSR). The remarkably similar time series pattern to the original time series can be reconstructed using the obtained parameters of all components. The EEG was recorded during all-night sleep on five consecutive nights in five healthy adults, by a total of 25 recordings. The variations of the height of successive 1-min delta components in the EEG were analyzed. In addition, two autocorrelograms were made for two time series patterns. These were reconstructed from two specific sets of the components obtained by the proposed analysis method. These autocorrelograms demonstrated a long-span variation with near double-REM-sleep interval in not a few records. Based on these data, it appears that the delta component of sleep EEG does not always demonstrate a simple gradually decreasing trend.

Sequential amplitude variations in alpha band component in human electroencephalograms during sleep onset

“…The EEG records were quantitatively analyzed using the RLSSR method, 18,19 which can calculate an arbitrary number of points and show discrete component values for amplitude and phase. The records in Frontal, F3, Central, C3, and Occipital, O1, were analyzed in this report.…”

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

“…The repeated least squares spectrum for residual (RLSSR) method was developed to analyze the long‐span variations of the delta‐component in sleep electroencephalograms 1 . While Fourier analysis is not appropriate for analyzing such data, which appear as one cycle pattern with a decreasing trend, the least squares spectrum (LSS) method 2 is understood to be effective.…”