Letter to the Editor: Analysis of Problematic Time Series with the LombÐScargle Method, A Reply to ‘Emphasizing Difficulties in the Detection of Rhythms with LombÐScargle Periodograms’

A large variety of time series analysis techniques is available for biological rhythm research, each with their own strengths and weaknesses. Even if a complete collection of all these techniques became available and easily accessible, and prerequisites, assumptions, strengths, weaknesses and problems of all of them were listed, then still it would not be easy to choose the optimal method for a particular set of data and a specific research question. The reason is that, in general, researchers do not know all the details about their time series (otherwise, analysis would not be necessary). In biological rhythm research it is often impossible, for instance, to know whether a time series is stationary (i.e., its statistical properties do not change over time). Also, it may be difficult or impossible to decide whether certain data points are outliers that need to be removed from the time series before analysis. Likewise, some analysis techniques require a priori knowledge about the statistical distribution of noise, and some techniques are more susceptible to deviations from the assumed distribution than others. These and many other factors usually make it impossible to be certain that a given analysis technique is the best for the task at hand. All the knowledge that is available about a time series, however, can and should be used to select an analysis technique that is, at the least, appropriate. This means that the prerequisites and assumptions of the chosen technique must not be violated by the data, or if they are, one must be sure that the effects of the violation(s) are minor (e.g., by checking the available literature or by conducting simulations) so that