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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Unevenly sampled sine waves, with a single period of seven days, are shown on the left. The corresponding periodograms are plotted on the right. Peaks with a period of seven days (ie. equal to a frequency of about 0.14 {days$^{-1}$}) can be seen in the periodograms. For low sample numbers, these peaks are very broad and are difficult to resolve. When the sample rates are higher, the peaks are much more distinct, and easy to detect.\relax }}{3}{figure.caption.1}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Estimated period using the Lomb-Scargle periodgram for a randomly sampled sine wave versus different numbers of samples in a period. The random sampling procedure is carried out twenty times for each sample number---the averages of the twenty results are plotted as red squares, and the error bars are calculated based the actual range of values observed. Clearly, periodogram estimation of period fails for low sample numbers. \relax }}{4}{figure.caption.2}}
\newlabel{fig2}{{2}{4}{Estimated period using the Lomb-Scargle periodgram for a randomly sampled sine wave versus different numbers of samples in a period. The random sampling procedure is carried out twenty times for each sample number---the averages of the twenty results are plotted as red squares, and the error bars are calculated based the actual range of values observed. Clearly, periodogram estimation of period fails for low sample numbers. \relax }{figure.caption.2}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces The corresponding $p$-values for a randomly sampled sine wave as a function of the numbers of samples in a period. The sampling procedure is carried out twenty times for each individual number of samples. Only the points under the green line indicate statistically significant periodicity. The error bars are calculated based on the actual range of values observed. \relax }}{5}{figure.caption.3}}
\newlabel{fig3}{{3}{5}{The corresponding $p$-values for a randomly sampled sine wave as a function of the numbers of samples in a period. The sampling procedure is carried out twenty times for each individual number of samples. Only the points under the green line indicate statistically significant periodicity. The error bars are calculated based on the actual range of values observed. \relax }{figure.caption.3}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces The corresponding $p$-values for sine waves with different periods from 2 to 15 days and with the sampling pattern used in Madondo's study is demonstrated. All the points are above of the green line that means Madondo's approach is not able to detect significant periodicity in this range. \relax }}{6}{figure.caption.4}}
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces The periodicity for (a) 19 purely random time-series and (b) 19 purely sinusoidal time-series are assessed using the null hypothesis that there is no periodicity. The pointwise lower one-sided 95\% confidence bound (red line) needs to exceed the null line (green dotted line) to suggest a significant peak. What this figure illustrates is that Madondo's mean periodogram approach may not be able to indicate periodicity in time-series with varying periods. \relax }}{7}{figure.caption.5}}
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