How to spot a "wave" in the graph of new Covid 19 cases In my dataset I have the daily number of new Covid 19 cases for many countries. I want to find an algorithm which will detect and calculate the number of "waves" which exist in the graph of new cases of every country. For example, in the below image  you can see that there is one big "wave". Does anyone know how to spot "waves" like this in a graph?
 A: There are a few statistical methods that can help you here:

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*Firstly, it might be more useful to show the number of cases on a logarithmic scale, since the magnitude of the waves and the surrounding noise oscillations appear to conform for that scale.  Start by creating an improved version of your graph with proper axis labelling (including units) and the vertical axis using a logarithmic scale.  This will give you a clearer idea of the magnitude of the humps when looked at in exponential-growth terms.


*In order to identify the waves, you need a method of decomposing your observed time-series into the waves and the noise.  A simple method to do this is to use smoothing but it is also possible to use formal statistical modelling to obtain an estimated signal and noise.


*Once you have an estimate of the underlying "signal" (either from a smoothing method or formal modelling) you will need to decide how big a hump constitutes a "wave".  For example, does the slight hump at approx 310-340 constitute a "wave"?  Here you will want to impose some criteria for deciding how big a hump qualifies.  From a statistical perspective, this might mean imposing a minimum requirement on the magnitude of the hump and then identifying a hump as a "wave" if it meets some inferential requirement for meeting that size (e.g., passes a one-sided hypothesis test for the magnitude at a chosen significance level).
