Onset time determination of precursory events in time series data by an extension of Singular Spectrum Transformation

To predict an occurrence of extraordinary phenomena, such as earthquakes, failures of engineering systems and financial market crushes, it is important to identify precursory events in time series. However, existing methods are limited in their applicability for real world precursor detections. Recently, Ide and Inoue [1] have developed an SSA-based change-point detection method, called singular spectrum transformation (SST). SST is suitable for detecting various types of change-points, but real world precursor detections can be far more difficult than expected. In general, precursory events are observed as minute and less-visible fluctuations preceding an onset of massive fluctuations of extraordinary phenomena and therefore they are easily over-looked. To overcome this point, we extend the conventional SST to the multivariable SST. The originality of our strategy is in focusing on synchronism detections of precursory events in multiple sequences of univariate time series. We performed some experiments by using artificial data and showed the superiority of multivariable SST in detecting onset of precursory events. Furthermore, the superiority is also shown statistically in determining the onset of precursory events by using real world time series.