Advances in Time-Series Analysis for Astronomy's Big Data Era

Emission of matter accreted on black holes (BHs) in active galactic nuclei (AGN) shows variability across the electromagnetic spectrum. Radio to gamma-ray band power spectral densities (PSDs) of AGN time-series are dominated by stochastic broadband noise typically modeled well with a Damped Random Walk or power-law functions. However, ongoing efforts have identified an increasing number of AGN candidates, for which a (quasi-)periodic PSD component appears to be statistically significant. AGN whose light show strong periodic modulations have become widely recognized as candidate BH binaries. Such binaries are a natural consequence of hierarchical structure formation, where galaxies grow via mergers. This talk will review efforts to characterize multi-wavelength AGN variability, including periodicities, in time domain with the Continuous-time Auto-Regressive Moving Average approaches, CARMA. Caveats related to non-stationary AGN time series, as well as novel avenues to overcome them, will be discussed in the light of anticipated massive single and binary AGN datasets from sky surveys delivered by observatories like Vera Rubin and others. 

The extreme dimming events observed in Betelgeuse in 2019-20 and RW Cephei in 2022 occurred suddenly following long periods of stable behavior. After these events, the stars have increased in brightness but have not returned to earlier behavior. Unobserved Components Models (UCM) provide a statistical method for analyzing changes in baseline characteristics such as these. UCM separates a light curve into periodic, baseline level, regression trend, and irregular components. This enables qualification and comparison of a star's behavior before, during, and after events such as those recently seen in Betelgeuse and RW Cephei. This analysis finds Betelgeuse has brightened since the dimming event, with a shorter period and an upward trend in brightness exceeding the previous baseline level. As of May 2023, Betelgeuse is found to have a V of 0.2 and a period of about 310 - 360 days, lower than the period of 400 - 425 days before the dimming event. The irregular variable RW Cephei is found to have a historical baseline magnitude of 7.01 ± 0.12. RW Cephei also has increased in brightness since its dimming event, from 7.75 at its faintest in early 2023 to 7.38 two months later. Source code for UCM analysis of variable stars is given in Python, R, and SAS. 

The prediction of extreme events in time series is a fundamental problem arising in many financial, scientific, engineering, and other applications. In this talk, I will present a general Neyman-Pearson-type characterization of optimal extreme event predictors in terms of density ratios. This characterization yields new insights and several closed-form optimal extreme event predictors for additive models. These results naturally extend to time series; I will discuss optimal extreme event prediction for heavy-tailed autoregressive and moving average models. Using a uniform law of large numbers for ergodic time series, we have established the asymptotic optimality of an empirical version of the optimal predictor for autoregressive models. Using multivariate regular variation, we have obtained expressions for the optimal extremal precision in heavy-tailed infinite moving averages, which provide theoretical bounds on the ability to predict extremes in this general class of models. I will close by describing the application of our theory and methodology to the important problem of solar flare prediction. Our results demonstrate the success and limitations of long-memory autoregressive as well as long-range dependent heavy-tailed FARIMA models for the prediction of extreme solar flares. 

I will discuss the problem of detecting and characterizing solar and stellar flares in time series data from multiple observatories. The flares occur stochastically, but are sometimes clustered, and always occur over an existing emission process which makes it difficult to disentangle them from baseline emission. I will discuss flares seen in high-energy X-ray data from the Chandra X-ray Observatory as well as optical light curves from TESS.