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## Discussion

We hope that the results of the previous section have convinced the reader that the naive least squares formulae provide only a lower limit to the errors, and that the true errors may be much higher. In practice, we have found that the actual errors in frequency can in some cases be a factor of 10 or more larger than those indicated by the formal least squares fits. The effect of correlations in the data is to increase the size of the errors. When the correlation time of the noise is short compared to the period of the signal, the least squares error estimates should be multiplied by the square root of the number of consecutive points which are correlated, . For noise with a correlation time of order the signal period, a more precise model for the correlations would be required. Of course in real data, we expect the noise to be comprised of several components, each with its own correlation time, as well as a component due to white noise. In conclusion, we wish to re-iterate that the naive formulae of the second section represent a lower bound only to the errors, and we urge strong skepticism in the application of these equations. If reliable error estimates are needed, then the correlations in the residuals must be examined in more detail before any statements can be made about the true sizes of the errors.
Acknowledgements. We would like to thank M. Breger and D. Kurtz for useful discussions.
References
Breger et al. 1999, A&A, in press
Koen, C. 1999, MNRAS, in press
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical Recipes in Fortran 77 (Cambridge, New York, Melbourne: Cambridge University Press)
Schwarzenberg-Czerny, A. 1991, MNRAS, 253, 198
Schwarzenberg-Czerny, A. 1999, APJ, 516, 315

Next: The new period determination Up: A derivation of the Previous: Correlated Noise
Wolfgang Zima
1999-09-09