Period Analysis using the Least Absolute Shrinkage and Selection Operator (Lasso)

Abstract

We introduced least absolute shrinkage and selection operator (lasso) in obtaining periodic signals in unevenly spaced time-series data. A very simple formulation with a combination of a large set of sine and cosine functions has been shown to yield a very robust estimate, and the peaks in the resultant power spectra were very sharp. We studied the response of lasso to low signal-to-noise data, asymmetric signals and very closely separated multiple signals. When the length of the observation is sufficiently long, all of them were not serious obstacles to lasso. We analyzed the 100-year visual observations of delta Cep, and obtained a very accurate period of 5.366326(16) d. The error in period estimation was several times smaller than in Phase Dispersion Minimization. We also modeled the historical data of R Sct, and obtained a reasonable fit to the data. The model, however, lost its predictive ability after the end of the interval used for modeling, which is probably a result of chaotic nature of the pulsations of this star. We also provide a sample R code for making this analysis.