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Elorrieta, F., Eyheramendy, S., & Palma, W. (2019). Discrete-time autoregressive model for unequally spaced time-series observations. Astron. Astrophys., 627, 11 pp.
Abstract: 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.
Keywords: methods: statistical; methods: data analysis; stars: general
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Elorrieta, F., Eyheramendy, S., Palma, W., & Ojeda, C. (2021). A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series. Mon. Not. Roy. Astron. Soc., 505(1), 1105–1116.
Abstract: 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 dependence in astronomical light curves consider the information of each band separately (e.g, CIAR, IAR, and CARMA models) disregarding the dependence 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 long-period variable stars and to distinguish between classes of stochastic objects, providing promising features that can be used for classification purposes.
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Lagos, F., Schreiber, M. R., Parsons, S. G., Zurlo, A., Mesa, D., Gansicke, B. T., et al. (2020). The White Dwarf Binary Pathways Survey -III. Contamination from hierarchical triples containing a white dwarf. Mon. Not. Roy. Astron. Soc., 494(1), 915–922.
Abstract: The White Dwarf Binary Pathways Survey aims at increasing the number of known detached A, F, G, and K main-sequence stars in close orbits with white dwarf companions (WD+AFGK binaries) to refine our understanding about compact binary evolution and the nature of Supernova Ia progenitors. These close WD+AFGK binary stars are expected to form through common envelope evolution, in which tidal forces tend to circularize the orbit. However, some of the identified WD+AFGK binary candidates show eccentric orbits, indicating that these systems are either formed through a different mechanism or perhaps they are not close WD+AFGK binaries. We observed one of these eccentric WD+AFGK binaries with SPHERE and find that the system TYC 7218-934-1 is in fact a triple system where the WD is a distant companion. The inner binary likely consists of the G-type star plus an unseen low-mass companion in an eccentric orbit. Based on this finding, we estimate the fraction of triple systems that could contaminate the WD+AFGK sample. We find that less than 15 per cent of our targets with orbital periods shorter than 100 d might be hierarchical triples.
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Sandford, E., Espinoza, N., Brahm, R., & Jordan, A. (2019). Estimation of singly transiting K2 planet periods with Gaia parallaxes. Mon. Not. Roy. Astron. Soc., 489(3), 3149–3161.
Abstract: When a planet is only observed to transit once, direct measurement of its period is impossible. It is possible, however, to constrain the periods of single transiters, and this is desirable as they are likely to represent the cold and far extremes of the planet population observed by any particular survey. Improving the accuracy with which the period of single transiters can be constrained is therefore critical to enhance the long-period planet yield of surveys. Here, we combine Gaia parallaxes with stellar models and broad-band photometry to estimate the stellar densities of K2 planet host stars, then use that stellar density information to model individual planet transits and infer the posterior period distribution. We show that the densities we infer are reliable by comparing with densities derived through asteroseismology, and apply our method to 27 validation planets of known (directly measured) period, treating each transit as if it were the only one, as well as to 12 true single transiters. When we treat eccentricity as a free parameter, we achieve a fractional period uncertainty over the true single transits of 94(-58)(+87) per cent, and when we fix e = 0, we achieve fractional period uncertainty 15(-6)(+30) per cent, a roughly threefold improvement over typical period uncertainties of previous studies.
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