Flexible and Scalable Methods for Quantifying Stochastic Variability in the Era of Massive Time-Domain Astronomical Data Sets

Abstract

We present the use of continuous-time autoregressive moving average (CARMA) models as a method for estimating the variability features of a light curve, and in particular its power spectral density (PSD). CARMA models fully account for irregular sampling and measurement errors, making them valuable for quantifying variability, forecasting and interpolating light curves, and for variability-based classification. We show that the PSD of a CARMA model can be expressed as a sum of Lorentzian functions, which makes them extremely flexible and able to model a broad range of PSDs. We present the likelihood function for light curves sampled from CARMA processes, placing them on a statistically rigorous foundation, and we present a Bayesian method to infer the probability distribution of the PSD given the measured lightcurve. Because calculation of the likelihood function scales linearly with the number of data points, CARMA modeling scales to current and future massive time-domain data sets. We conclude by applying our CARMA modeling approach to light curves for an X-ray binary, two AGN, a long-period variable star, and an RR-Lyrae star, in order to illustrate their use, applicability, and interpretation.

18 pages, 16 figures, in press at ApJ. Revised to match accepted version. Code for utilizing the CARMA models is at https://github.com/bckelly80/carma_pack

References in corpus (8)

• Modelling the behaviour of accretion flows in X-ray binaries
• Modeling the Time Variability of SDSS Stripe 82 Quasars as a Damped Random Walk
• The Sloan Digital Sky Survey-II Supernova Survey: Technical Summary
• Is Quasar Optical Variability a Damped Random Walk?
• Quasar Selection Based on Photometric Variability
• A novel variability-based method for quasar selection: evidence for a rest frame ~54 day characteristic timescale
• Variability-based AGN selection using image subtraction in the SDSS and LSST era
• Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes

Cited by in corpus (170)

• Understanding the Lomb-Scargle Periodogram
• Fast and scalable Gaussian process modeling with applications to astronomical time series
• Active Galactic Nuclei: what's in a name?
• The Kepler Catalog of Stellar Flares
• A systematic search for close supermassive black hole binaries in the Catalina Real-Time Transient Survey
• False periodicities in quasar time-domain surveys
• Stingray: A Modern Python Library For Spectral Timing
• Periodograms for Multiband Astronomical Time Series
• A Population of Short-Period Variable Quasars from PTF as Supermassive Black Hole Binary Candidates
• The Sloan Digital Sky Survey Reverberation Mapping Project: Technical Overview
• A characteristic optical variability timescale in astrophysical accretion disks
• Revisiting Stochastic Variability of AGNs with Structure Functions
• Are the Variability Properties of the Kepler AGN Light Curves Consistent with a Damped Random Walk?
• Stochastic modelling of star-formation histories II: star-formation variability from molecular clouds and gas inflow
• Understanding extreme quasar optical variability with CRTS: I. Major AGN flares
• Optical variability of AGN in the PTF/iPTF survey
• Pan-STARRS1 variability of XMM-COSMOS AGN. II. Physical correlations and power spectrum analysis
• Limitations on the recovery of the true AGN variability parameters using Damped Random Walk modeling
• Stochastic modeling of star-formation histories I: the scatter of the star-forming main sequence
• Improving Damped Random Walk parameters for SDSS Stripe 82 Quasars with Pan-STARRS1
• Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. VIII. Structure of the Broad-Line Region and Mass of the Central Black Hole in Mrk 142
• Testing the binary hypothesis: pulsar timing constraints on supermassive black hole binary candidates
• Autoregressive Times Series Methods for Time Domain Astronomy
• Stochastic modeling of multiwavelength variability of the classical BL Lac object OJ 287 on timescales ranging from decades to hours
• Corona-Heated Accretion-disk Reprocessing (CHAR): A Physical Model to Decipher the Melody of AGN UV/optical Twinkling
• Optical Variability of Quasars with 20-Year Photometric Light Curves
• Discovery of a ~5 day characteristic timescale in the Kepler power spectrum of Zw 229-15
• Gamma-ray quasi-periodicities of blazars. A cautious approach
• Mid-IR Variability and Dust Reverberation Mapping of Low-$z$ Quasars. I. Data, Methods and Basic Results
• The remarkable X-ray variability of IRAS 13224-3809 I: The variability process
• AGN Variability Analysis Handbook
• A class of multi-resolution approximations for large spatial datasets
• Vecchia approximations of Gaussian-process predictions
• Quasi-periodicities of BL Lac Objects
• Examining AGN UV/optical Variability Beyond the Simple Damped Random Walk
• A comprehensive power spectral density analysis of astronomical time series I: the Fermi-LAT gamma-ray light curves of selected blazars
• Three Lyman-alpha emitting galaxies within a quasar proximity zone at z=5.8
• Extracting Information from AGN Variability
• Candidate Periodically Variable Quasars from the Dark Energy Survey and the Sloan Digital Sky Survey
• Testing the relativistic Doppler boost hypothesis for supermassive black hole binary candidates
• EUCLIA - Exploring the UV/optical continuum lag in active galactic nuclei. I. a model without light echoing
• AGN Continuum Reverberation Mapping Based on Zwicky Transient Facility Light Curves
• The Chandra Deep Fields: Lifting the Veil on Distant Active Galactic Nuclei and X-Ray Emitting Galaxies
• Opacity Driven Convection and Variability in Accretion Disks around Supermassive Black Holes
• Near Infrared Variability of obscured and unobscured X-ray selected AGN in the COSMOS field
• How far is quasar UV/optical variability from damped random walk at low frequency?
• Characteristic Variability Timescales in the Gamma-ray Power Spectra of Blazars
• Looking at Blazar Light Curve Periodicities with Gaussian Processes
• Winds Can "Blow Up" AGN Accretion Disk Sizes
• Gaussian Process Modeling $Fermi$-LAT $\gamma$-ray Blazar Variability: A Sample of Blazars with $\gamma$-ray Quasi-periodicities
• A Comprehensive Power Spectral Density Analysis of Astronomical Time Series. II. The Swift/BAT Long Gamma-Ray Bursts
• A Non-parametric Approach to Constrain the Transfer Function in Reverberation Mapping
• Discovery of a Candidate Binary Supermassive Black Hole in a Periodic Quasar from Circumbinary Accretion Variability
• Two transient X-ray Quasi-Periodic Oscillations separated by an intermediate state in 1H 0707-495
• Deepest view of AGN X-ray variability with the 7 Ms Chandra Deep Field-South survey
• Toward the unambiguous identification of supermassive binary black holes through Bayesian inference
• Studies in Astronomical Time Series Analysis: VII. An Enquiry Concerning Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions
• A Quasi-periodic Oscillation in the gamma-ray Emission from the Non-blazar Active Galactic Nucleus PKS 0521-36
• Robust Identification of Active Galactic Nuclei through HST Optical Variability in GOODS-S: Comparison with the X-ray and mid-IR Selected Samples
• Optical Variability of the Dwarf AGN NGC 4395 from the Transiting Exoplanet Survey Satellite
• The QUEST-La Silla AGN Variability Survey: selection of AGN candidates through optical variability
• AutoRegressive Planet Search: Methodology
• Spitzer Observations of Long Term Infrared Variability Among Young Stellar Objects in Chamaeleon I
• A physical model for the UV/optical power spectra of AGN
• Evolution of quasar stochastic variability along its main sequence
• Untangling Optical Emissions of the Jet and Accretion Disk in the Flat-Spectrum Radio Quasar 3C 273 with Reverberation Mapping Data
• Multiwavelength variability power spectrum analysis of the blazars 3C 279 and PKS 1510-089 on multiple timescales
• A Fast, 2D Gaussian Process Method Based on Celerite: Applications to Transiting Exoplanet Discovery and Characterization
• Modeling Stochastic Variability in Multi-Band Time Series Data
• Mira variables in the Milky Way's nuclear stellar disc: discovery and classification
• An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves
• A Full Characterisation of the Supermassive Black Hole in IRAS 09149-6206
• Modeling Quasar UV/Optical Variability with the Corona-heated Accretion-disk Reprocessing (CHAR) Model
• Blazar Variability: A Study of Non-stationarity and the Flux-RMS Relation
• A Method to Measure the Unbiased Decorrelation Timescale of the AGN Variable Signal from Structure Functions
• Core shift effect in blazars
• Expectations for time-delay measurements in active galactic nuclei with the Vera Rubin Observatory
• Searching for quasi-periodic oscillations in astrophysical transients using Gaussian processes
• Modeling photometric reverberation mapping data for the next generation of big data surveys. Quasar accretion disks sizes with the LSST
• Keplerian periodogram for Doppler exoplanets detection: optimized computation and analytic significance thresholds
• The Timescale-Dependent Color Variability of Quasars Viewed with GALEX
• Rapid parameter estimation of a two-component neutron star model with spin wandering using a Kalman filter
• AGN STORM 2. VII. A Frequency-resolved Map of the Accretion Disk in Mrk 817: Simultaneous X-ray Reverberation and UVOIR Disk Reprocessing Time Lags
• Photometric detection of internal gravity waves in upper main-sequence stars. III. Comparison of amplitude spectrum fitting and Gaussian process regression using celerite2
• X-ray Reverberation Mapping of Ark 564 using Gaussian Process Regression
• A falling Corona model for the anomalous behavior of the broad emission lines in NGC 5548
• Aldebaran b's temperate past uncovered in planet search data
• Radio Monitoring Campaigns of Six Strongly Lensed Quasars
• LSST Cadence Strategy Evaluations for AGN Time-series Data in Wide-Fast-Deep Field
• The Curious Case of PHL 293B: A Long-Lived Transient in a Metal-Poor Blue Compact Dwarf Galaxy
• The nature of the soft-excess and spectral variability in the Seyfert 1 galaxy Zw 229.015
• Discrete-time autoregressive model for unequally spaced time-series observations
• X-ray/UVOIR Frequency-resolved Time Lag Analysis of Mrk 335 Reveals Accretion Disk Reprocessing
• A Gravitationally Lensed Quasar Discovered in OGLE
• Kepler light curve analysis of the blazar W2R 1926+42
• Optical follow-up of the tick-tock massive black hole binary candidate
• Do the Kepler AGN Light Curves Need Re-processing?
• A 6.4yr optical quasi-periodic oscillations in SDSS J075217.84+193542.2: a new candidate for central binary black hole system
• Incorporating Measurement Error in Astronomical Object Classification
• A New Approach for Measuring Power Spectra and Reconstructing Time Series in Active Galactic Nuclei
• Chemical evolution of local post-starburst galaxies: Implications for the mass-metallicity relation
• Discovering the Mass-Scaled Damping Timescale from Microquasars to Blazars
• Modeling the Variability of Active Galactic Nuclei by Infinite Mixture of Ornstein-Uhlenbeck(OU) Processes
• Reliable Identification of Binary Supermassive Black Holes from Rubin Observatory Time-Domain Monitoring
• Ensemble power spectral density of SDSS quasars in UV/optical bands
• No Evidence for Periodic Variability in the Light Curve of Active Galaxy J0045+41
• How can the optical variation properties of active galactic nuclei be unbiasedly measured?
• Variable classification in the LSST era: Exploring a model for quasi-periodic light curves
• Systematic evaluation of variability detection methods for eROSITA
• On Granulation and Irregular Variation of Red Supergiants
• Continuum optical-UV and X-ray variability of AGN: current results and future challenges
• Lensed quasar search via time variability with the HSC transient survey
• Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties
• Periodicity in the continua and broad line curves of a quasar E1821+643
• Techniques for Finding Close-in, Low-mass Planets around Subgiants
• A 3.8yr optical quasi-periodic oscillations in blue quasar SDSS J132144+033055 through combined light curves from CSS and ZTF
• A new timescale-mass scaling for the optical variation of active galactic nuclei across the intermediate-mass to supermassive scales
• Ornstein-Uhlenbeck parameter extraction from light curves of Fermi-LAT observed blazars
• Using Leaked Power to Measure Intrinsic AGN Power Spectra of Red-Noise Time Series
• Probing the disc-jet coupling in S4 0954+65, PKS 0903-57, & 4C +01.02 with $\gamma$-rays
• Search for periodicities in High Energy AGNs with a time-domain approach
• Novel bivariate autoregressive model for predicting and forecasting irregularly observed time series
• Statistical analysis on X-ray flares from the nucleus and HST-1 knot in the M87 jet
• Systematic research of low redshift optically selected SDSS Type-2 AGN but with apparent long-term optical variabilities from Catalina Sky Survey, I: data sample and basic results
• TD-CARMA: Painless, accurate, and scalable estimates of gravitational-lens time delays with flexible CARMA processes
• Search for X-ray Quasi-periodicity of six AGNs using Gaussian Process method
• Tracking hidden magnetospheric fluctuations in accretion-powered pulsars with a Kalman filter
• Selection of Burst-like Transients and Stochastic Variables Using Multi-Band Image Differencing in the Pan-STARRS1 Medium-Deep Survey
• Dwarf AGNs from Variability for the Origins of Seeds (DAVOS): Optical Variability of Broad-line Dwarf AGNs from the Zwicky Transient Facility
• Testing the Cosmological Principle: On the Time Dilation of Distant Sources
• Origins of the UV/X-ray Relation in Arakelian 120
• Revisiting radio variability of the blazar 3C 454.3
• A candidate of binary black hole system in AGN with broad Balmer emission lines having quite different line widths
• Strong Lensed QSOs with Variability Detectable by LSST: How many are there?
• Temperature Fluctuations in Quasar Accretion Discs from Spectroscopic Monitoring Data
• Long-term variability of the composite galaxy SDSS J103911-000057: A candidate of true Type-2 AGN
• Modelling variability power spectra of active galaxies from irregular time series
• Examining AGN UV/Optical Variability Beyond the Simple Damped Random Walk. II. Insights from 22 Years Observations of SDSS, PS1 and ZTF
• X-ray reverberation modelling of the continuum, optical/UV time-lags in quasars
• Stochastic modeling of the time variability of ALMA calibrators
• On the Origin of the Dramatic Spectral Variability of WPVS 007
• Do Cellular Automaton Avalanche Models Simulate the Quasi-Periodic Pulsations of Solar Flares?
• K2 Optical Emission from OJ 287 and Other Gamma-Ray Blazars on Hours-to-Weeks Timescales from 2014-2018
• The detection of possible $\gamma$-ray quasi-periodic modulation with $\sim$600 days from the blazar S2 0109+22
• The Performance of Photometric Reverberation Mapping at High Redshift and the Reliability of Damped Random Walk Models
• Optical variability of ICRF3 quasars in the Pan-STARRS 3Pi survey with functional principal components analysis
• Time domain methods for X-ray and gamma-ray astronomy
• AutoRegressive Planet Search: Feasibility Study for Irregular Time Series
• Fourier Domain
• Scalable and Robust Multiband Modeling of AGN Light Curves in Rubin-LSST
• State-space representation of Matérn and Damped Simple Harmonic Oscillator Gaussian processes
• Continuum polarization reverberation mapping of AGNs
• Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and $H_0$ inference
• Variability Signatures of a Burst Process in Flaring Gamma-ray Blazars
• SDSSJ14584479+3720215: A Benchmark JHK Blazar Light Curve from the 2MASS Calibration Scans
• Amoeba: An AGN Model of Optical Emissions Beyond steady-state Accretion discs
• The Feasibility and Flexibility of Selecting Quasars by Variability Using Ensemble Machine Learning Algorithms
• State Space Modelling for detecting and characterising Gravitational Waves afterglows
• Variability as a new discovery channel for Intermediate-Mass Black Holes in the Time Domain Era
• Decadal Variability Survey in MACSJ1149
• Detection of quasars in the time domain
• Six Maxims of Statistical Acumen for Astronomical Data Analysis
• Scalable Gaussian Processes for Integrated and Overlapping Measurements Via Augmented State Space Models
• Variability Study and Searching for QPOs with day-like periods in the blazar S5 0716+714 with TESS
• Periodic Variable Stars Modulated by Time-Varying Parameters
• AT 2021hdr: A candidate tidal disruption of a gas cloud by a binary super massive black hole system
• Optical Variability Structure Function of Low-Luminosity AGN using ATLAS Lightcurves
• Probing extreme black-hole outflows on short timescales via high spectral-resolution X-ray imagers
• Seeing through the dust: Unraveling near-infrared variability in type 2 active galactic nuclei
• AGILE: an end-to-end Rubin-LSST simulation of AGNs, galaxies, and stars I. Software description and first data release