I am interested in analyzing epidemiological time-series with wavelets. The data is about a particular infectious disease from 1994-2008.
First the count data was normalized with the square root transformation, after which I proceeded to the wavelet analysis. The analysis was done on this web page: http://ion.researchsystems.com/.
Although the results are quite neat, I really don't know how to interpret them. Therefore I would be glad if someone would take the time to make sense of it :)
Matej
I'vr long had an interest in wavelets. I'll take a closer look at this next week.
Please keep me informed.
Rick
Not an expert in wavelets but i think the challenge is in interpreting the signal properties - amplitude and phase and whether these have any meaning in epidemiological sense. For example, the amplitude could indicate limits at which the disease level never exceed? what does the oscillation pattern indicate (are there parameters controlling this?) and more important what could be driving the process. The phase may have similar properties. -
I have pratically no experience with wavelet analysis. I cannot therefore be of any help.
Hi Matej - In a nutshell, wavelets on time series allow you to identify “regime changes” with respect to the periodicity. For example, it helps answering: "As time goes by, is incidence of the disease shifting from an annual period to a biannual one?"
At a glance on the graph you attached, we could naively say (looking at the red areas representing the strongest power) the data has a strong signal related to a 32-months period during the first 20 months, then some kind of a transition regime between 20-30 months time points where the strongest signal is 32- or 12-month period. Then, the data enters a regime of a 12-month period during the time points 30 to 70 months. Beyond the 70 months time point, there does’t seem to have a clear periodicity in this time series… That’s a super-light analysis of course, but again, the idea is to identify "trends of periodicity” in your time series.
A brief note: you seem to have small cases counts: the max of your sqr-root data is 5 so max 25 cases. That’s not a lot and you may be dealing with a very noisy data set, hampering the wavelet analysis.
I hope this helps.
David
Matej, this paper (and many more) has good explanation and interpretation. It was done by Professor Masahiro. You can contact him personally should you be interested in knowing more. I have attended his lectures several times:
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0060001
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