A module for modelling strictly periodic signals in time series, based on Hogg & Villar, 2021. Most of the linear algebra that is presented here for the regression work is expanded upon in the above text, so we refer the reader there.
- C. Johnston: Royal Society | University of Surrey / KU Leuven / Max Planck Institute for Astrophysics
- D.W. Hogg: New York University / Center for Computational Astrophysics | Flatiron Institute / Max Planck Institute for Astronomy
- N.L. Eisner: Tatari Inc. / Center for Computational Astrophysics | Flatiron Institute / Princeton University
Periodic (seasonal) signals are ubiquitous to time series data. However, there are a wide variety of (well motivated) methods used by various teams for modelling different periodic signals that make the results often difficult to compare. What's more is that many of these methods are very computationally expensive. Puffins is designed to be a method for modelling the (strictly) periodic signals present in time series data by way of a linear regression model imbued with a feature embedding and weighting. By utilizing a feature embedding and weighting, Puffins models a time series using a Fourier basis and solves for a data driven model that only retains important features due to the feature weighting.
By providing a uniform basis on which to flexibly model different types of periodic signals, Puffins naturally provides a uniform bases on which we can compare and classify the signals based on the modelled regression coefficients. In addition to providing a modelling frame work, we will also provide a classification framework based on the modelling output that can either used in conjunction with the regression model, independently of it, or not at all.
Developing this package was motivated by modelling the signatures of eclipsing binary stars in astronomical photometric time series data. While there are highly sophisticated, physically motivated, parameteric modelling codes built specifically for modelling eclipsing binary stars to an extremely high precision, they are often high dimensional models, with strong parameter degeneracies, and are imensely computationally costly. While some science cases demand extremely high precision parameter estimates, other workflows such as classification and residual modelling are hampered by the high computation cost of modelling the high amplitude eclipsing binary signal. Thus, we have a clear motive to build effective models to model and remove the eclipse signal from astronomical time series data.
Well, the naming logic is as follows: Who doesn't like Puffins? No one.