Automatic and Accurate Determination of the Onset Time of the Quasi-periodic Oscillation

Abstract

The identification of the start (onset) time of the quasi-periodic oscillation (QPO), which is called the Pi 2 pulsations in a magnetospheric physics, from the ground magnetic field observation is usually carried out by focusing on a wave- like component obtained by applying a linear band-pass filter [5], [6]. When the background magnetic field (i.e. time-dependent meanvalue structure) and/or the amplitude of high-frequency components (i.e., time-dependent variance structure) change rapidly around the initial period of Pi 2 pulsations, any linear band-pass filter, which also includes the procedure based on a simple modification of the wavelet analysis, always generates a pseudo precursor prior to a true onset time. In such a case, an accurate determination of onset time requires a nonlinear filter which enables us to separate only the wavy-like component associated with Pi 2 pulsations from the time-varying mean and/or variance structures with various discontinuities. In this study we introduce a locally fixed time series model which partitions the time series into three segments and to model each segment as the linear combination of several possible components. An optimal partition obtained by the minimum AIC procedure allows us to determine an onset time precisely even for the above-mentioned case. We illustrate this procedure by showing an application to actual data sets.