I present source codes that were used in the following paper:

Efficient Period Search for Time Series Photometry
(Min-Su Shin and Yong-Ik Byun, JKAS, 37, 79, 2004)
We developed an algorithm to identify and determine periods of variable sources. With its robustness and high speed, it is expected to become an useful tool for surveys with large volume of data. This new scheme consists of an initial coarse process of finding several candidate periods followed by a secondary process of much finer period search. With this multi-step approach, best candidates among statistically possible periods are produced without human supervision and also without any prior assumption on the nature of the variable star in question. We tested our algorithm with 381 stars taken from the ASAS survey and the result is encouraging. In about 76% cases, our results are nearly identical as their published periods. Our algorithm failed to provide convincing periods for only about 10% cases. For the remaining 14%, our results significantly differ from their periods. We show that, in many of these cases, our periods are superior and much closer to the true periods. However, the existence of failures, and also periods sometimes worse than manually controlled results, indicates that this algorithm needs further improvement. Nevertheless, the present experiment shows that this is a positive step toward a fully automated period analysis for future variability surveys.
ADS | PDF

The code used in the paper is composed of two parts: a rough period estimation by analysis of variance and polynomial function fitting and a refined determination of period using spline interpolation. The original code of the first part has been developed by Alex Schwarzenberg-Czerny and I modified the code for my research. You can get the orginal code from his web page. Carl W. Akerlof has developed an original code of the second part. The code was also modified and combined with the first part in my research. I am thankful that Alex and Carl permit me to post the related codes here.

Application of cubic splines to the spectral analysis of unequally spaced data
(Akerlof et al., ApJ, 436, 787, 1994) : ADS
ROTSE All-Sky Surveys for Variable Stars. I. Test Fields
(Akerlof et al., AJ, 119, 1901, 2000) : ADS
Carl's code

On the advantage of using analysis of variance for period search
(Schwarzenberg-Czerny, MNRAS, 241, 153, 1989) : ADS
Fast and Statistically Optimal Period Search in Uneven Sampled Observations
(Schwarzenberg-Czerny, ApJ, 460, 107, 1996) : ADS
Alex's code

The package posted on this web page is exactly same as that used in my paper

You can download my code:
[Current stable version: ver 3.5 released in Aug. 2013] MS_Period.tar.gz | README
(Please, check the README file before you download or install the code as well as the paper.)
The current version supporting OpenMP has been developed to exploit the current CPUs that have multiple cores. For the object shown in the following plots, the version with OpenMP support with 8 cores is about 11 times faster than the serial version, comparing wall-clock time.

(the example raw light curve)

(the light curve in phase space with the found period 0.435801 day)

(the periodogram with multi-harmonic function fitting)

(the periodogram with phase folding and AoV)

The following light curve is used to test the methods. The correct period is 34.3 days.

(the periodogram with multi-harmonic function fitting)

(the periodogram with phase folding and AoV)

You can freely modify and distribute the codes that are not parts of Carl or Alex's original work. But please, let me know what you changed or what kind of problems you have.

I am really grateful for the permission of Carl W. Akerlof and Alex Schwarzenberg-Czerny to post the parts of their codes on this web page. Please, cite their relevant papers as well as mine when you use the codes.

You might be interested in the following papers and codes too.

"A FAST CHI-SQUARED TECHNIQUE FOR PERIOD SEARCH OF IRREGULARLY SAMPLED DATA" David M. Palmer 2009 ApJ 695 496-502
http://public.lanl.gov/palmer/fastchi.html

The VARTOOLS Light Curve Analysis Program (developed by Joel D. Hartman)
http://www.cfa.harvard.edu/~jhartman/vartools/

Period04 (developed by Patrick Lenz)
http://www.univie.ac.at/tops/Period04/index.html

The following paper also might be useful. The paper summarizes various statistics for period estimation.
- On period determination methods, Heck, A., Manfroid, J., & Mersch, G., 1985, A&A Suppl. Ser., 59, 63
- Periodicity detection in irregularly sampled light curves by robust regression and outlier detection, Thieler et al., 2013, Statistical Analysis and Data Mining, Volume 6, Issue 1, pages 73-89

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Period estimation by the minimum length method

This method is discussed well in Dworetsky (1983) . Simply, if a trial period is correct, the phase diagram with the trial period must produce a well-aligned light curve in phase space having the least length. The file Period_length.tar.gz includes a source code and a simple shell script. But the file doesn't include "minmax" program which is also used in the above package. Please, check the explanation given in the README file for the above package. This method is quite fast. I do not build an OpenMP version for this code. In addition to the scaling rule of magnitude recomended in Dworetsky (1983), I added seven different scaling methods (see the source code). The following plots show the example distribution of lengths for a range of trial periods with the sine light curves.
(scaling 0) (scaling 1) (scaling 2) (scaling 3) (scaling 4) (scaling 5) (scaling 6) (scaling 7) (scaling 8)
This method works well with this well-sampled sine curve. But when I applied this method to the above example with the period 0.435801 day, the method couldn't find the correct period as shown in the following plots of length distribution for trial periods.
(scaling 0) (scaling 1) (scaling 2) (scaling 3) (scaling 4) (scaling 5) (scaling 6) (scaling 7) (scaling 8)

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Period estimation by using the String/Rope length method with the Kafler-Kinman statistic

This approach was explained in Clarke (2002). In principle, this statistic is same as von Neumann statistic. The code can be downloaded. The following figures show periodograms with this method for the above two examples of the sine curve and the ASAS light curve.

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Detecting variability in astronomical time-series data

The idea of this multi-step approach is basically based on the fact that a correct period is not found by only statistical measurements without physical nature of variable objects. Prof. Yong-Ik Byun and I intended to develope this package with consideration of detecting variable objects in time-series data and classifying them together. The detection of variable objects has been discussed in a related conference proceeding

Variability Detection of Time Series Data in the Virtual Observatory Era
(7th Pacific Rim Conference on Stellar Astrophysics, 2005) (PPT file) | (PDF file)

Infinite Gaussian Mixture models and clustering methods have been applied to discover new variable candidates:
Detecting variability in massive astronomical time series data - I. Application of an infinite Gaussian mixture model, Shin et al., 2009, MNRAS, 400, 1897,
Detecting Variability in Massive Astronomical Time-series Data. II. Variable Candidates in the Northern Sky Variability Survey, Shin et al., 2012, AJ, 143, 65.

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Some notes on developing the codes

I have tried to follow the Unix philosophy when developing various codes.
"Write programs that do one thing and do it well. Write programs to work together. Write programs to handle text streams, because that is a universal interface." - Doug McIlroy
(see Wikipedia about the Unix philosophy.)
Therefore, there are many parts of the codes that you can optimize for your specific work. The current codes support only basic features. User interface has not been a main focus. You can also increase speed by improving I/O parts of the codes.

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Min-Su Shin (msshin @ kasi.re.kr)