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I am using the Lomb-Scargle code to estimate some frequencies in a short time-series, the time series is shown in the first image. The results of the Lomb-Scargle analysis are shown in the second, and I have zoomed in on a prominent peak at about 2 cycles per day. However this peak is smeared and thus it is proving difficult to resolve the real frequency of this component. Is there any other methods, or improvements to the method I am using, to accurately resolve the important frequency components within this short time-series?

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There is some information on the use of methods for short time series here but its not clear whether they need to be regularly sampled. Ideally I am looking for a method that works with irregularly sampled data, from some research it appears that maximum entropy methods are the answer, but I am not sure whether these have been implemented in MATLAB? Although from the this link, it appears that there is an equivalent method, 'The Yule-Walker AR method produces the same results as a maximum entropy estimator. However again its not clear whether the data need to be uniformly sampled?

user2653752
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  • I think the peak looks pretty sharp. Why do you think this is not right? You can always test the result of the by manually calculating the periods. You can't expect a needle-looking peak if your cycles have themselves variations. –  Feb 13 '15 at 12:38
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    Also, the methods presented in the MATLAB documentation page talk about sampling frequency so - yes, they assume the series to be uniformly sampled. As a work-around for non-uniformly-sampled series there's always the possibility of re-sampling with interpolation. –  Feb 13 '15 at 12:42
  • Just to clarify, the Lomb Scargle method does not require uniformly sampled data [link](http://uk.mathworks.com/matlabcentral/fileexchange/22215-lomb-normalized-periodogram). The plots above used this method. Looking at the bottom diagram, the periodogram seems to show a wide peak, with a flat top between 1.95 and 2.05 cycles per day. That equates to about 12.31hrs to 11.71hrs, I am hoping to resolve it better than that. – user2653752 Feb 13 '15 at 12:56
  • Maybe I should clarify too: you were wondering about the sampling requirements of the functions mentioned in the MATLAB Signal Processing Toolbox page, this being the link that you posted: http://uk.mathworks.com/help/signal/ug/spectral-analysis.html I wasn't referring to Lomb-Scargle. Also, you are quick to assign the cause of "flat" peak to an error inherent in the method. Are you sure that the data itself doesn't present variations in the same range? This can be easily done by manually calculating the length of some cycles in your data, and checking the value of their periods. –  Feb 13 '15 at 13:27
  • That is certainly worth a try, would the dominant period, i.e. at approximately 1 day not obscure the smaller periods when using the manual method. I don't mean to assign the problem to an error in the method, but I am aware that there are well known problems with spectral analysis for short time series, for example: http://www.ncbi.nlm.nih.gov/pubmed/24400700 – user2653752 Feb 13 '15 at 13:44
  • Can you make your data available? – A. Donda Feb 17 '15 at 01:26
  • I could do, not sure how to host it on stack exchange though. – user2653752 Feb 18 '15 at 09:14

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