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Peranso offers a wide variety of period analysis methods, so an obvious question is: which method should I use for which type of object? Unfortunately, there is no universal method that works best for every object. Each method makes its own assumptions about the data and the shape of the light curve, and therefore has its own strengths and blind spots.
A large comparison study by Graham et al.¹ illustrates this well. Using real observations from three sky surveys rather than simulated data, they found that even the best algorithms recover the correct period of a regular periodic variable at best about 50% of the time. Their performance depends strongly on the type of object and the quality of the light curve, and aliases and harmonics of the true period remain the most common source of error. Conditional Entropy performed best overall in that study.
The practical lesson is that choosing the right method matters, but checking the result matters even more. This chapter therefore gives guidelines for both.
Before you start
- Look at the light curve first. Draw it and inspect its shape: is it smooth or does it have sharp features (eclipses, outbursts, flares)? Is the amplitude constant? Are there trends? A visual inspection often reveals more than any algorithm, and it tells you which method is likely to work.
- Data quality limits every method. Few observations, large errors or big gaps produce less reliable results, whatever method you use.
- Your data must cover enough cycles. A period can only be determined reliably if the data cover at least two, and preferably many more, cycles. Treat any period longer than about half the total time span of your data with suspicion. Some methods (notably Conditional Entropy) then tend to “find” a period equal to the length of the data set.
- Know your sampling. Ground-based observations are taken at night, so they are spaced by about one day. This creates aliases at ±1 cycle/day (and at ±1 cycle per sidereal day) around the true frequency. Long seasonal gaps create aliases too.
- Magnitude errors matter for some methods. GLS, BGLS, FALC, ANOVA, CCC and PDC-E use the errors of the observations. Make sure they are realistic.
Choosing a method
Three questions largely determine the best choice:
- What does the light curve look like? Sinusoidal methods (Lomb-Scargle, GLS, BGLS, DFT, DCDFT) are very sensitive to smooth, sine-like variations, but they perform poorly on light curves with sharp features such as narrow eclipses. Shape-independent methods (ANOVA, PDM, Phase-binned AoV, CE, string-length methods, CCC, PDC-E) make no or few assumptions about the shape.
- How many observations do you have, and how are they spread? With many well-sampled observations, most methods work. With few or sparse observations, PDM, PDC-E and CCC are good choices, and EASolver for eclipsing binaries with only a few points in eclipse.
- What are you looking for? One period, several periods, a period that changes over time, or transits?
The table below gives a starting point for common types of objects. Always try at least two methods from different families.
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Object type
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First choice
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Notes
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Pulsating stars with smooth light curves
(δ Scuti, smooth Cepheids)
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GLS, ANOVA
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Use CLEANest or prewhitening if multi-periodic.
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RR Lyrae and Cepheids
(sawtooth light curves)
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ANOVA, PDC-E, CCC
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Sinusoidal methods may favour harmonics.
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Eclipsing binaries (EA, EB, EW)
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ANOVA, CE
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Often found at P/2: always check 2P. For CE with narrow eclipses, use Nb ≈ 20.
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EA binaries with few points in eclipse (survey data)
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EASolver
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Cataclysmic variables (superhumps, orbital humps)
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GLS, ANOVA, CCC
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Detrend outburst decline first.
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Rotational and spotted variables
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GLS, BGLS
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Spot evolution can change the period slightly over time.
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Long-period and semi-regular variables (Miras, SR)
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DCDFT, CLEANest
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Data must cover many cycles.
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Multi-periodic stars
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CLEANest
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Period changing over time
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WWZ
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Asteroid rotation
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FALC
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FALC is the de facto standard for asteroid light curves.
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Exoplanet transits
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EEBLS
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Sparse data with any light curve shape
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PDC-E, CCC
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Strengths and limitations per family
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Family
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Methods
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Strengths
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Limitations
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Fourier
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DFT, DCDFT, CLEANest, Bloomfield
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Fast. Well suited to multi-periodic stars (CLEANest).
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Assume sinusoids. Power spreads over harmonics for non-sinusoidal light curves.
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Least-squares fit
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Lomb-Scargle, GLS, FALC, ANOVA
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Sensitive. FALC and ANOVA also handle non-sinusoidal shapes.
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Lomb-Scargle and GLS assume a sinusoid.
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Bayesian
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BGLS
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Gives the relative probability of peaks.
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Assumes a sinusoid. Needs realistic magnitude errors.
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Phase dispersion
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PDM, Jurkevich, Phase-binned AoV, AoV Transit, CE
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Independent of light curve shape. CE handles aliases well.
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Results depend on the bin settings (Nb, Nc).
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String length
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Lafler-Kinman, Renson, Dworetsky
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Simple; work with few observations.
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Sensitive to noise.
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Statistical dependence
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PDC-E
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Shape-independent; no parameters; strong on sparse data.
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Calculation time grows with the square of the number of observations.
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Specific purpose
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EEBLS, EASolver, WWZ
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Designed for transits, EA binaries and period changes respectively.
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Only suited to their purpose.
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Cross-cycle prediction
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CCC
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Shape-independent; uses magnitude errors; compares only different cycles, which suppresses aliases within a night; robust against outliers.
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Needs features that are observed in at least two cycles; information from a single run carries little weight. Slower than Fourier methods. Still experimental.
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Checking your results
Whatever method you use, never accept the highest peak blindly:
- Compare methods. Run at least two methods from different families. If they agree, your confidence increases. If they disagree, find out why. Note that agreement between methods is a useful check, but no guarantee: Graham et al. found that combining methods does not by itself perform better than the best individual method.
- Check harmonics and aliases. Fold your data on the best period P, and also on 2P, P/2 and the ±1 cycle/day aliases. The correct period gives the cleanest and most physically plausible phase diagram. Eclipsing binaries with two similar eclipses are the classic case: most methods find P/2.
- Inspect the phase diagram. A true period gives a coherent phase diagram, without systematic offsets between nights or data sets.
- Determine the uncertainty and the significance. Use Peranso’s period error calculation and the significance (False Alarm Probability) analysis. A period from one or two nights of data may be correct, but it has a large uncertainty.
- Watch out for the period of your sampling. Peaks near 1 day (and its fractions) or near the length of your data set are usually caused by the sampling, not by the star.
A personal note
In developing Peranso, I have studied hundreds of light curves of many different objects. Although there is no universal period analysis method, there is one that in my experience comes pretty close: ANOVA. I have been amazed by its ability to improve peak detection sensitivity and to damp alias periods. Try it on your data, and compare it with one of the other methods. That combination of an excellent method and a critical check is the best route to a reliable period.
(1) Graham, M.J., Drake, A.J., Djorgovski, S.G., Mahabal, A.A., Donalek, C., Duan, V., Maker, A., 2013, Mon. Not. R. Astron. Soc., 434, 3423
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