RobPer {RobPer}

Periodogram based on (robustly) fitting a periodic function to a light curve

Description

Calculates a periodogram by fitting a periodic function to a light curve, using a possibly robust regression technique and possibly taking into account measurement accuracies. See RobPer-package for more information about light curves. For a lot of more details see Thieler, Fried and Rathjens (2016) and Thieler et al. (2013).

Usage

RobPer(ts, weighting, periods, regression, model, steps = 10, tol = 1e-03,
 var1 = weighting, genoudcontrol = list(pop.size = 50, max.generations = 50,
 wait.generations = 5), LTSopt =TRUE, 
 taucontrol = list(N = 100, kk = 2, tt = 5, rr = 2, approximate = FALSE),
 Scontrol=list(N = ifelse(weighting,200,50), kk = 2, tt = 5, b=.5, cc = 1.547,
 seed = NULL) )

Arguments

ts

dataframe or matrix with three (or two) numeric columns containing the light curve to be analyzed: observation times (first column), observed values (second column), measurement accuracies (thirs column). If it is intended to calculate the periodogram of a time series without measurement accuracies (weighting=FALSE), the third column may be omitted.

weighting

logical: Should measurement accuracies be taken into account performing weighted regression?

periods

vector of positive numeric values: Trial periods.

regression

character string specifying the regression method used: Possible choices are "L2" (least squares regression using the R-function lm, package stats), "L1" (least absolute deviation regression, using the R-function rq, package quantreg), "LTS" (least trimmed squares regression, using the R-function ltsReg, package robustbase), "huber" (M-regression using the Huber function), "bisquare" (M-regression using the bisquare function), "S" (S-regression using adapted code from Salibian-Barrera and Yohai 2006, see FastS), "tau" (tau-regression using adapted code from Salibian-Barrera, Willems and Zamar 2008, see FastTau).

model

character string specifying the periodic function fitted to the light curve: Possible choices are "step" (periodic step function), "2step" (two overlapping periodic step functions, see Details), "sine" (sine function), "fourier(2)" and "fourier(3)" (Fourier series of second or third degree), "splines" (periodic spline function with four B-splines per cycle, generated using spline.des, package splines).

steps

integer value: Number of steps per cycle for the periodic step function(s).

tol

(small) positive number: Precision for convergence criteria. Used in case of regression="huber" or "bisquare" or if regression="LTS" and LTSopt=TRUE.

var1

logical: Should variance estimate be set to 1 in case of weighted M-regression?

genoudcontrol

list of three integers pop.size, max.generations, wait.generations: Control parameters for the R-function genoud, package rgenoud, see Details and Mebane Jr. and Sekhon (2011). Used in case of regression="bisquare" or if regression="LTS" and LTSopt=TRUE.

LTSopt

logical: In case of LTS-regression, should regression result of ltsReg be optimized using the R-function genoud, package rgenoud?

taucontrol

list of four integer values N, kk, tt, rr and one logical approximate: Control parameters for the R-function FastTau. For more details see FastTau and Salibian-Barrera, Willems and Zamar (2008).

Scontrol

list of three integers N, kk and tt, two positive numbers b and cc and another integer seed: Control parameters for the R-function FastS. For more details see FastS and Salibian-Barrera and Yohai (2006). Please notice that the further Scontrol entry int expected by FastS is automatically set to FALSE in order to let RobPer work properly.

Details

For each trial period, a periodic function (defined by model) is fitted to the light curve using regression technique regression. The periodogram bar is the coefficient of determination. In case of model="2step", two different step functions with opposed jumping times are fitted separately and the periodogram bar is the mean of both coefficients of determination. For a lot of more details see Thieler, Fried and Rathjens (2016) and Thieler et al. (2013).

Value

numeric vector: Periodogram bars related to the trial periods.

Note

Performing weighting = FALSE, regression="L2", model="sine" on a equidistantly sampled time series is equivalent to calculating the standard periodogram of Fourier analysis, see Example.

Performing regression="L2", model="sine" is equivalent to calculating a Generalized Lomb-Scargle periodogram (see Zechmeister and Kürster 2009).

Performing regression="L2", model="step" is equivalent to calculating an Epoch Folding (Leahy et al. 1983) or Anaysis of Variance (Schwarzenberg-Czerny 1989) periodogram.

Performing regression="L2", model="2step" is equivalent to calculating a Phase Dispersion Minimization periodogram (Stellingwerf 1978).

A former version of this function is used in Thieler et al. (2013). For more equivalences see there.

Author(s)

Anita M. Thieler, Jonathan Rathjens and Roland Fried

References

Leahy, D. A., Darbro, W., Elsner, R. F., Weisskopf, M. C., Kahn, S., Sutherland, P. G. and Grindlay, J. E. (1983): On Searches for Pulsed Emission with Application to Four Globular Cluster X-ray Sources-NGC 1851, 6441, 6624, and 6712. The Astrophysical Journal, 266 (1), 160-170

Mebane Jr., W. R. and Sekhon, J. S. (2011): Genetic Optimization Using Derivatives: The rgenoud Package for R. Journal of Statistical Software, 42 (11), 1-26

Salibian-Barrera, M. and Yohai, V. (2006): A Fast Algorithm for S-Regression Estimates. Journal of Computational and Graphical Statistics, 15 (2), 414-427

Salibian-Barrera, M., Willems, G. and Zamar, R. (2008): The Fast-tau Estimator for Regression. Journal of Computational and Graphical Statistics, 17 (3), 659-682

Stellingwerf, R. F. (1978): Period Determination Using Phase Dispersion Minimization. The Astrophysical Journal, 224, 953-960

Thieler, A. M., Backes, M., Fried, R. and Rhode, W. (2013): Periodicity Detection in Irregularly Sampled Light Curves by Robust Regression and Outlier Detection. Statistical Analysis and Data Mining, 6 (1), 73-89

Thieler, A. M., Fried, R. and Rathjens, J. (2016): RobPer: An R Package to Calculate Periodograms for Light Curves Based on Robust Regression. Journal of Statistical Software, 69 (9), 1-36, <doi:10.18637/jss.v069.i09>

Zechmeister, M. and Kürster, M. (2009): The Generalised Lomb-Scargle Periodogram. A New Formalism for the Floating-Mean and Keplerian Periodograms. Astronomy and Astrophysics, 496 (2), 577-584

See Also

Applies FastS and FastTau, Xgen, examples in RobPer-package and TK95_uneq.

Examples

# For more examples see RobPer-package and TK95_uneq!

# Example to show the equivalence between the periodogram from Fourier analysis
# and the Lomb-Scargle periodogram in case of equidistant sampling and equal weighting:
set.seed(7)
n <- 120
# equidistant time series:
zr <- tsgen(ttype="equi", ytype="const", pf=1, redpart= 0, s.outlier.fraction=0.2, 
    interval=FALSE, npoints=n, ncycles=n, ps=1, SNR=1, alpha=1.5)
# periodogram of Fourier analysis
PP_konv <- spec.pgram(zr[,2], taper = 0,pad = 0, fast = FALSE, demean = TRUE,
    detrend = TRUE, plot = TRUE)
# Lomb-Scargle periodogram - Note: Due to the regression ansatz,
# RobPer is not able to compute period 2 in this case.
PP_new <- RobPer(ts=zr, weighting=FALSE, periods=1/PP_konv$freq,
    regression="L2", model="sine")
plot(PP_konv$freq, PP_konv$spec, ylab="periodogram", xlab="frequency",
    main="Comparison of RobPer(...regression='LS', model='sine') and spec.pgram")
points(PP_konv$freq, PP_new*var(zr[,2])*n/2, type="l")
legend("top",lty=c(1,0), pch=c(-5,1), legend=c("RobPer*var(y)*n/2", "spec.pgram"))
# Due to different ways of computation, the scaled periodograms are not exactly
# identical, but show very similar behavior.