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Susana Eyheramendy

Publications and source records attributed to Susana Eyheramendy.

17 recordsLinked to original sources
arXiv2026

Earth and space observations meet complex algebras: from complex to octonions for multivariate autoregressive time series analysis

Many datasets arise as multivariate time series observed at irregular time intervals, particularly in Earth observation and astronomical measurements. Classical time-series models assume that time is discrete and observations occur at equally spaced intervals, limiting their ability to capture dynamics when observation gaps vary. Existing approaches to irregular sampling rely on continuous-time formulations, which assume that observation intervals are sufficiently small. We address this limitation by introducing a discrete-time framework that accommodates irregular observation gaps while preserving multivariate dependence structures. We introduce a framework for the analysis of irregularly observed multivariate time series based on hypercomplex autoregressive processes. The framework embeds multivariate observations into a hypercomplex algebraic structure, allowing multiple variables and their interactions to be represented within a single mathematical entity while incorporating irregular observation gaps. The resulting process admits a structured matrix representation, which enables the model to be expressed as a state-space system. This formulation provides an estimation methodology in which model parameters can be inferred using Kalman filtering techniques. The state-space representation allows recursive estimation and prediction in the presence of irregular sampling intervals. The performance of the methodology is illustrated through data and applications to remote sensing and astronomical datasets, where observations occur at nonuniform time intervals. The results demonstrate that the approach captures dynamics and cross-variable interactions difficult to model using traditional time-series techniques. The proposed framework provides a methodology for analyzing irregularly sampled multivariate time series and opens possibilities for modeling observational data across disciplines.

stat.ME↗
arXiv2025

Novel SIMEX algorithm for autoregressive models to estimate AGN variability

The origin of the variability in accretion disks of active galactic nuclei (AGN) is still unknown, but its behavior can be characterized by modeling the time series of optical wavelength fluxes coming from the accretion disks with damped random walk (DRW) being the most popular model for this purpose. The DRW is modeled by a characteristic fluctuation amplitude and damping timescale τ, with the latter being potentially related to the mass and accretion rate onto the massive black hole. The estimation of τ is challenging, with commonly used methods such as the maximum likelihood (ML) and the least square error (LSE) resulting in biased estimators. This problem arises most commonly for three reasons: i) the light curve has been observed with additive noise; ii) some cadence scheme; iii) when the autocorrelation parameter is close to one. The latter is called the unit root problem. In order to improve these parameter estimation procedures for estimating τ, we developed a simulation-extrapolation (SIMEX) methodology in the context of time series analysis. We consider both the standard class of autoregressive processes observed at regular intervals and a recently developed class of irregularly autoregressive processes (iAR). The performance of the SIMEX estimation method was evaluated under conditions of near-unit-root behavior and additive noise through extensive Monte Carlo simulations. Monte Carlo experiments confirm that the SIMEX approach outperforms MLE and LSE methods, offering a reduction in estimation bias ranging from 30% to 90%. Real-data applications further validate the methodology, yielding better model fits and lower mean squared errors (MSE). The more accurate estimation of the damping timescale parameter can help to better understand the currently tentative links between DRW and physical parameters in AGN.

astro-ph.IM↗
arXiv2024

TOI-4504: Exceptionally large Transit Timing Variations induced by two resonant warm gas giants in a three planet system

We present a joint analysis of TTVs and Doppler data for the transiting exoplanet system TOI-4504. TOI-4504 c is a warm Jupiter-mass planet that exhibits the largest known transit timing variations (TTVs), with a peak-to-node amplitude of $\sim$ 2 days, the largest value ever observed, and a super-period of $\sim$ 930 d. TOI-4504 b and c were identified in public TESS data, while the TTVs observed in TOI-4504 c, together with radial velocity (RV) data collected with FEROS, allowed us to uncover a third, non-transiting planet in this system, TOI-4504 d. We were able to detect transits of TOI-4504 b in the TESS data with a period of 2.4261$\pm 0.0001$ days and derive a radius of 2.69$\pm 0.19$ R$_{\oplus}$. The RV scatter of TOI-4504 was too large to constrain the mass of TOI-4504 b, but the RV signals of TOI-4504 c \& d were sufficiently large to measure their masses. The TTV+RV dynamical model we apply confirms TOI-4504 c as a warm Jupiter planet with an osculating period of 82.54$\pm 0.02$ d, mass of 3.77$\pm 0.18$ M$_{\rm J}$ and a radius of 0.99$\pm 0.05$ R$_{\rm J}$, while the non-transiting planet TOI-4504 d, has an orbital period of 40.56$\pm 0.04$ days and mass of 1.42$_{-0.06}^{+0.07}$ M$_{\rm J}$. We present the discovery of a system with three exoplanets: a hot sub-Neptune and two warm Jupiter planets. The gas giant pair is stable and likely locked in a first-order 2:1 mean-motion resonance (MMR). The TOI-4504 system is an important addition to MMR pairs, whose increasing occurrence supports a smooth migration into a resonant configuration during the protoplanetary disk phase.

astro-ph.EP↗
arXiv2023

Online estimation methods for irregular autoregressive models

In the last decades, due to the huge technological growth observed, it has become increasingly common that a collection of temporal data rapidly accumulates in vast amounts. This provides an opportunity for extracting valuable information through the estimation of increasingly precise models. But at the same time it imposes the challenge of continuously updating the models as new data become available. Currently available methods for addressing this problem, the so-called online learning methods, use current parameter estimations and novel data to update the estimators. These approaches avoid using the full raw data and speeding up the computations. In this work we consider three online learning algorithms for parameters estimation in the context of time series models. In particular, the methods implemented are: gradient descent, Newton-step and Kalman filter recursions. These algorithms are applied to the recently developed irregularly observed autoregressive (iAR) model. The estimation accuracy of the proposed methods is assessed by means of Monte Carlo experiments. The results obtained show that the proposed online estimation methods allow for a precise estimation of the parameters that generate the data both for the regularly and irregularly observed time series. These online approaches are numerically efficient, allowing substantial computational time savings. Moreover, we show that the proposed methods are able to adapt the parameter estimates quickly when the time series behavior changes, unlike batch estimation methods.

cs.LG↗
arXiv2022

The Next Generation Virgo Cluster Survey. XXXIII. Stellar Population Gradients in the Virgo Cluster Core Globular Cluster System

We present a study of the stellar populations of globular clusters (GCs) in the Virgo Cluster core with a homogeneous spectroscopic catalog of 692 GCs within a major axis distance $R_{\rm maj} = $ 840 kpc from M87. We investigate radial and azimuthal variations in the mean age, total metallicity, [Fe/H], and $α$-element abundance, of blue (metal-poor) and red (metal-rich) GCs using their co-added spectra. We find that the blue GCs have a steep radial gradient in [Z/H] within $R_{\rm maj} =$ 165 kpc, with roughly equal contributions from [Fe/H] and [$α$/Fe], and flat gradients beyond. By contrast, the red GCs show a much shallower gradient in [Z/H], which is entirely driven by [Fe/H]. We use GC-tagged Illustris simulations to demonstrate an accretion scenario where more massive satellites (with more metal- and $α$-rich GCs) sink further into the central galaxy than less massive ones, and where the gradient flattening occurs because of the low GC occupation fraction of low-mass dwarfs disrupted at larger distances. The dense environment around M87 may also cause the steep [$α$/Fe] gradient of the blue GCs, mirroring what is seen in the dwarf galaxy population. The progenitors of red GCs have a narrower mass range than those of blue GCs, which makes their gradients shallower. We also explore spatial inhomogeneity in GC abundances, finding that the red GCs to the northwest of M87 are slightly more metal-rich. Future observations of GC stellar population gradients will be useful diagnostics of halo merger histories.

astro-ph.GA↗
arXiv2022

A Novel First-Order Autoregressive Moving Average Model to Analyze Discrete-Time Series Irregularly Observed

A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the general case, it is shown that the model is weakly stationary. The lowest dimension of the state-space representation is given along with the one-step linear predictors and their mean squared errors. The maximum likelihood estimation procedure is discussed, and their finite-sample behavior is assessed through Monte Carlo experiments. These experiments show that bias, root mean squared error, and coefficient of variation are smaller when the length of the series increases. Further, the method provides good estimations for the standard errors, even with relatively small sample sizes. Also, the irregularly spaced times seem to increase the estimation variability. The application of the proposed model is made through two real-life examples. The first is concerned with medical data, whereas the second describes an astronomical data set analysis.

stat.ME↗
arXiv2021

Alert Classification for the ALeRCE Broker System: The Real-time Stamp Classifier

We present a real-time stamp classifier of astronomical events for the ALeRCE (Automatic Learning for the Rapid Classification of Events) broker. The classifier is based on a convolutional neural network, trained on alerts ingested from the Zwicky Transient Facility (ZTF). Using only the \textit{science, reference} and \textit{difference} images of the first detection as inputs, along with the metadata of the alert as features, the classifier is able to correctly classify alerts from active galactic nuclei, supernovae (SNe), variable stars, asteroids and bogus classes, with high accuracy ($\sim$94\%) in a balanced test set. In order to find and analyze SN candidates selected by our classifier from the ZTF alert stream, we designed and deployed a visualization tool called SN Hunter, where relevant information about each possible SN is displayed for the experts to choose among candidates to report to the Transient Name Server database. From June 26th 2019 to February 28th 2021, we have reported 6846 SN candidates to date (11.8 candidates per day on average), of which 971 have been confirmed spectroscopically. Our ability to report objects using only a single detection means that 70\% of the reported SNe occurred within one day after the first detection. ALeRCE has only reported candidates not otherwise detected or selected by other groups, therefore adding new early transients to the bulk of objects available for early follow-up. Our work represents an important milestone toward rapid alert classifications with the next generation of large etendue telescopes, such as the Vera C. Rubin Observatory.

astro-ph.IM↗
arXiv2021

An irregularly spaced first-order moving average model

A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed data and the specification of second-order moments. The second definition provided is more flexible in the sense that it allows for considering other distributional assumptions. The statistical properties are investigated along with the one-step linear predictors and their mean squared errors. It is established that the process is strictly stationary under normality and weakly stationary in the general case. Maximum likelihood and bootstrap estimation procedures are discussed and the finite-sample behavior of these estimates is assessed through Monte Carlo experiments. In these simulations, both methods perform well in terms of estimation bias and standard errors, even with relatively small sample sizes. Moreover, we show that for non-Gaussian data, for t-Student and Generalized errors distributions, the parameters of the model can be estimated precisely by maximum likelihood. The proposed IMA model is compared to the continuous autoregressive moving average (CARMA) models, exhibiting good performance. Finally, the practical application and usefulness of the proposed model are illustrated with two real-life data examples.

math.ST↗
arXiv2021

Novel bivariate autoregressive model for predicting and forecasting irregularly observed time series

In several disciplines it is common to find time series measured at irregular observational times. In particular, in astronomy there are a large number of surveys that gather information over irregular time gaps and in more than one passband. Some examples are Pan-STARRS, ZTF and also the LSST. However, current commonly used time series models that estimate the time dependency in astronomical light curves consider the information of each band separately (e.g, CIAR, IAR and CARMA models) disregarding the dependency that might exist between different passbands. In this paper we propose a novel bivariate model for irregularly sampled time series, called the bivariate irregular autoregressive (BIAR) model. The BIAR model assumes an autoregressive structure on each time series, it is stationary, and it allows to estimate the autocorrelation, the cross-correlation and the contemporary correlation between two unequally spaced time series. We implemented the BIAR model on light curves, in the g and r bands, obtained from the ZTF alerts processed by the ALeRCE broker. We show that if the light curves of the two bands are highly correlated, the model has more accurate forecast and prediction using the bivariate model than a similar method that uses only univariate information. Further, the estimated parameters of the BIAR are useful to characterize LongPeriod Variable Stars and to distinguish between classes of stochastic objects, providing promising features that can be used for classification purposes

astro-ph.IM↗
arXiv2019

Discrete-time autoregressive model for unequally spaced time-series observations

Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuous-time autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discrete-time process. We show that the model is weakly stationary and that it can be represented as a state-space system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.

astro-ph.IM↗
arXiv2018

An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves

Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually modeled using a parametric and/or physical model that assumes independent and homoscedastic errors, but in many cases these assumptions are not accurate and there remains a temporal dependency structure on the errors. This can occur, for example, when the proposed model cannot explain all the variability of the data or when the parameters of the model are not properly estimated. In this work we define an autoregressive model for irregular discrete-time series, based on the discrete time representation of the continuous autoregressive model of order 1. We show that the model is ergodic and stationary. We further propose a maximum likelihood estimation procedure and assess the finite sample performance by Monte Carlo simulations. We implement the model on real and simulated data from Gaussian as well as other distributions, showing that the model can flexibly adapt to different data distributions. We apply the irregular autoregressive model to the residuals of a transit of an extrasolar planet to illustrate errors that remain with temporal structure. We also apply this model to residuals of an harmonic fit of light-curves from variable stars to illustrate how the model can be used to detect incorrect parameter estimation.

astro-ph.IM↗
arXiv2018

The Next Generation Virgo Cluster Survey (NGVS) XXXI. The kinematics of intra-cluster globular clusters in the core of the Virgo cluster

Intra-cluster (IC) populations are expected to be a natural result of the hierarchical assembly of clusters, yet their low space densities make them difficult to detect and study. We present the first definitive kinematic detection of an IC population of globular clusters (GCs) in the Virgo cluster, around the central galaxy, M87. This study focuses on the Virgo core for which the combination of NGVS photometry and follow-up spectroscopy allows us to reject foreground star contamination and explore GC kinematics over the full Virgo dynamical range. The GC kinematics changes gradually with galactocentric distance, decreasing in mean velocity and increasing in velocity dispersion, eventually becoming indistinguishable from the kinematics of Virgo dwarf galaxies at $\mathrm{R>320\, kpc}$. By kinematically tagging M87 halo and intra-cluster GCs we find that 1) the M87 halo has a smaller fraction ($52\pm3\%$) of blue clusters with respect to the IC counterpart ($77\pm10\%$), 2) the $(g'-r')_{0}$ vs $(i'-z')_{0}$ color-color diagrams reveal a galaxy population that is redder than the IC population that may be due to a different composition in chemical abundance and progenitor mass, and 3) the ICGC distribution is shallower and more extended than the M87 GCs, yet still centrally concentrated. The ICGC specific frequency, $S_{N,\mathrm{ICL}}=10.2\pm4.8$, is consistent with what is observed for the population of quenched, low-mass galaxies within 1~Mpc from the cluster's center. The IC population at Virgo's center is thus consistent with being an accreted component from low-mass galaxies tidally stripped or disrupted through interactions, with a total mass of $\mathrm{M_{ICL,tot}=10.8\pm0.1\times10^{11}M_{\odot}}$.

astro-ph.GA↗
arXiv2018

A Near-infrared RR Lyrae census along the southern Galactic plane: the Milky Way's stellar fossil brought to light

RR Lyrae stars (RRLs) are tracers of the Milky Way's fossil record, holding valuable information on its formation and early evolution. Owing to the high interstellar extinction endemic to the Galactic plane, distant RRLs lying at low Galactic latitudes have been elusive. We attained a census of 1892 high-confidence RRLs by exploiting the near-infrared photometric database of the VVV survey's disk footprint spanning $\sim$70$^\circ$ of Galactic longitude, using a machine-learned classifier. Novel data-driven methods were employed to accurately characterize their spatial distribution using sparsely sampled multi-band photometry. The RRL metallicity distribution function (MDF) was derived from their $K_s$-band light curve parameters using machine-learning methods. The MDF shows remarkable structural similarities to both the spectroscopic MDF of red clump giants and the MDF of bulge RRLs. We model the MDF with a multi-component density distribution and find that the number density of stars associated with the different model components systematically changes with both the Galactocentric radius and vertical distance from the Galactic plane, equivalent to weak metallicity gradients. Based on the consistency with results from the ARGOS survey, three MDF modes are attributed to the old disk populations, while the most metal-poor RRLs are probably halo interlopers. We propose that the dominant [Fe/H] component with a mean of $-1$ dex might correspond to the outskirts of an ancient Galactic spheroid or classical bulge component residing in the central Milky Way. The physical origins of the RRLs in this study need to be verified by kinematical information.

astro-ph.SR↗
arXiv2016

A machine learned classifier for RR Lyrae in the VVV survey

Variable stars of RR Lyrae type are a prime tool to obtain distances to old stellar populations in the Milky Way, and one of the main aims of the Vista Variables in the Via Lactea (VVV) near-infrared survey is to use them to map the structure of the Galactic Bulge. Due to the large number of expected sources, this requires an automated mechanism for selecting RR Lyrae,and particularly those of the more easily recognized type ab (i.e., fundamental-mode pulsators), from the 10^6-10^7 variables expected in the VVV survey area. In this work we describe a supervised machine-learned classifier constructed for assigning a score to a K_s-band VVV light curve that indicates its likelihood of being ab-type RR Lyrae. We describe the key steps in the construction of the classifier, which were the choice of features, training set, selection of aperture and family of classifiers. We find that the AdaBoost family of classifiers give consistently the best performance for our problem, and obtain a classifier based on the AdaBoost algorithm that achieves a harmonic mean between false positives and false negatives of ~7% for typical VVV light curve sets. This performance is estimated using cross-validation and through the comparison to two independent datasets that were classified by human experts.

astro-ph.IM↗
arXiv2013

A Ground-based Optical Transmission Spectrum of WASP-6b

We present a ground based optical transmission spectrum of the inflated sub-Jupiter mass planet WASP-6b. The spectrum was measured in twenty spectral channels from 480 nm to 860nm using a series of 91 spectra over a complete transit event. The observations were carried out using multi-object differential spectrophotometry with the IMACS spectrograph on the Baade telescope at Las Campanas Observatory. We model systematic effects on the observed light curves using principal component analysis on the comparison stars, and allow for the presence of short and long memory correlation structure in our Monte Carlo Markov Chain analysis of the transit light curves for WASP-6. The measured transmission spectrum presents a general trend of decreasing apparent planetary size with wavelength and lacks evidence for broad spectral features of Na and K predicted by clear atmosphere models. The spectrum is consistent with that expected for scattering that is more efficient in the blue, as could be caused by hazes or condensates in the atmosphere of WASP-6b. WASP-6b therefore appears to be yet another massive exoplanet with evidence for a mostly featureless transmission spectrum, underscoring the importance that hazes and condensates can have in determining the transmission spectra of exoplanets.

astro-ph.EP↗
arXiv2007

A flexible Bayesian generalized linear model for dichotomous response data with an application to text categorization

We present a class of sparse generalized linear models that include probit and logistic regression as special cases and offer some extra flexibility. We provide an EM algorithm for learning the parameters of these models from data. We apply our method in text classification and in simulated data and show that our method outperforms the logistic and probit models and also the elastic net, in general by a substantial margin.

stat.ME↗