Detection of low level periodic signals through enhanced self-correlation method. The case of ER Vulpeculae


The self-correlation (SC) method proposed three decades ago by Percy, Jakate and Matthews is a complementary time series analysis method which provides a characterization of a variability phenomenon and an estimation of the involved time-scale. It can be applied to periodic, quasi-periodic and irregular phenomena, for either evenly or unevenly sampled data. An important deficiency of this method – mentioned by Percy himself – is the fact that the statistical properties of the SC are unknown so that the statistical significance of an ‘observed’ (quasi-)periodicity cannot be estimated.

In this paper, we investigate analytically and numerically the properties of the SC of a harmonic periodic signal by taking into account the influence of the finite length of the data set, the non-equidistant sampling, and the presence of an additive Gaussian white noise. This method is used to investigate the already inferred periodic modulation of the orbital period of the eclipsing binary system ER Vul.

In addition, we propose an improvement of the SC method by applying the ‘stacking method’ already used in seismology, which we call the enhanced SC (ESC) method. A statistical test relying on the ESC method together with Monte Carlo simulations allow us to claim the presence of a deterministic component at a significantly higher confidence level than that obtained through a Fourier based method.

The evaluation of the detectability of the ER Vul periodic phenomenon through the ESC method provides similar results as those previously obtained using the Fourier based method.


M. Crăciun
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

C. Vamoș
-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

A. Pop


Methods: data analysis; statistical methods, Self-correlation function, Monte Carlo simulations; stars: ER Vulpeculae.

Cite this paper as:

M. Crăciun, C. Vamoş, A. Pop, Detection of low level periodic signals through enhanced self-correlation method. The case of ER Vulpeculae, Monthly Notices of the Royal Astronomical Society, 448, 2066-2076 (2015)
DOI: 10.1093/mnras/stv108.



Not available yet.

About this paper

Print ISSN


Online ISSN






[1] Appourchaux T., 2004, A&A, 428, 1039

[2] Appourchaux T., 2011, in Pere L. P., Cesar E., eds, Asteroseismology. Cambridge Univ. Press, Cambridge, p. 123

[3] Black D. C., Scargle J. D., 1982, ApJ, 263, 854[4] Horne J. H., Baliunas S. L., 1986, ApJ, 302, 757[5] Johnson D. H., 2013, Statistical Signal Processing,

[6] Kuschnig R., Weiss W. W., Gruber R., Bely P. Y., Jenkner H., 1997, A&A, 328, 544

[7] Levy B. C., 2008, Principles of Signal Detection and Parameter Estimation. Springer-Verlag, Berlin

[8] Marinova M., Percy J. R., 1999, J. Am. Assoc. Var. Star Obs., 27, 122

[9] Percy J. R., 2007, Understanding Variable Stars. Cambridge Univ. Press, Cambridge

[10] Percy J. R., Long J., 2010, J. Am. Assoc. Var. Star Obs., 38, 161

[11] Percy J. R., Mohammed F., 2004, J. Am. Assoc. Var. Star Obs., 32, 9

[12] Percy J. R., Palaniappan R., 2006, 35, 290

[13] Percy J. R., Sen L., 1991, Inf. Bull. Var. Stars, 3670

[14] Percy J. R., Terziev E., 2011, J. Am. Assoc. Var. Star Obs., 39, 162

[15] Percy J. R., Jakate S. M., Matthews J. M., 1981, AJ, 86, 53

[16] Percy J. R., Ralli J. A., Sen L. V., 1993, PASP, 105, 287

[17] Percy J. R., Hosik J., Kincaide H., Pang C., 2002, PASP, 114, 551

[18] Percy J. R., Hosik J., Leigh N. W. C., 2003, PASP, 115, 59

[19] Percy J. R., Favaro E., Glasheen J., Ho B., 2004, Using Astrolab Selfcorrelation Software.∼percy/manual.pdf

[20] Percy J. R., Molak A., Lund H., Overbeek D., Wehlau A. F., Williams P. F., 2006a, PASP, 118, 805

[21] Percy J. R., Gryc W. K., Wong J. C.-Y., Herbst W., 2006b, PASP, 118, 1390

[22] Percy J. R., Esteves S., Glasheen J., Lin A., Long J., Mashintsova M., Terziev E., Wu S., 2010, J. Am. Assoc. Var. Star Obs., 38, 151

[23] Pop A., 1996, Rom. Astron. J., 6, 147

[24] Pop A., 1999, Inf. Bull. Var. Stars, 4801, 1

[25] Pop A., Vamos¸ C., 2013, New Astron., 23–24, 27

[26] Pop A., Vamos¸ C., Turcu V., 2010, AJ, 139, 425 Scargle J. D., 1982, ApJ, 263, 835

[27] Schwarzenberg-Czerny A., 1993, in Grosbøl P. J., de Ruijsscher R. C. E., eds, Proc. of 5th ESO/ST-ECF, Data Analysis Workshop, No. 47, Garching b. Munchen: European Southern Observatory, p. 149 Schwarzenberg-Czerny A., 1998,

[28] Balt. Astron., 7, 43

[29] Schwarzenberg-Czerny A., 2003, in Sterken C., ed., ASP Conf. Ser. Vol. 292, Interplay of Periodic, Cyclic and Stochastic Variability in Selected Areas of the H-R Diagram. Astron. Soc. Pac., San Francisco, p. 383

[30] Shearer P. M., 2009, Introduction to Seismology, 2nd edn. Cambridge Univ. Press, Cambridge Sturrock P. A., Scargle J. D., 2009, ApJ, 706, 393

[31] Vamos¸ C., Craciun M., 2012, Automatic Trend Estimation. Springer-Verlag, Berlin

[32] Welsh W. F., 1997, in Maoz D., Sternberg A., Leibowitz E. M., eds, Astrophysics and Space Science Library, Vol. 218, Astronomical Time Series, Measuring Variability in the Presence of Noise. Kluwer, Dordrecht, p. 171



Related Posts