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

We introduced least absolute shrinkage and selection operator (Lasso) in obtaining periodic signals in unevenly spaced time-series data. A very simple formulation with the combination of a large set of sine and cosine functions has been shown to yield a very robust estimate; also, 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 was 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 the period estimation was several times smaller than in the 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 the chaotic nature of the pulsations of this star. We also provided a sample R code for making this analysis.