Measuring Deviation from Stochasticity in Time-Series Using Autoencoder Based Time-Invariant Representation: Application to Black Hole Data

We propose a novel approach to quantify "deviation from stochasticity" (DS) in a time-series. This is important to determine if the time-series is coming from a physical phenomenon or if it is noise. This approach utilizes time-invariant representation obtained using time- and frequency-domain analyses. Autoencoder based time-invariant features have been utilized to obtain multi-scale reconstruction as well as identification of prominent peaks in dissimilarity curves. We devise a DS measure based on the observation that a stochastic time-series exhibits similar behavior across multiple time scales. The values of DS are expected to be significantly small for stochastic time-series in comparison with those for non-stochastic time-series, leading to classification. As proof of concept, we illustrate this trend on synthetic data. Subsequently, the proposed methodology is applied on astronomical data which are 12 distinct temporal classes of time-series pertaining to the black hole GRS 1915 + 105, obtained from RXTE satellite. This dataset had been previously studied using correlation integration (CI) based approach to understand the underlying dynamics leading to time-series classification. Results obtained using the proposed methodology are compared with those obtained using CI. Concurrence is obtained for 11 temporal classes, while one is found to be non-concurrent. This could be attributed to the observation that the non-concurrence is due to that specific time-series exhibiting both stochastic and non-stochastic characteristics. Besides, these DS values can also be interpreted as quantification of signal-to-noise ratio (SNR) of a time-series.