"Autocorrelation is essentially the convolution of a function with the same function reversed in time."

Source: http://documents.wolfram.com/applications/signals/Mathematic...

EDIT: This means that autocorrelation can be calculated using a Fourier transform, so essentially you'd be using it anyway.

The power-spectral density is the fourier-transform of the autocorrelation of a time series. So yes, it is the transform dual. But doing the straight autocorrelation immediately gives you the number of lags before the series repeats itself and is probably the best way to attack that type of problem.

The best way to attack that problem is by using common sense, some women have very heavy periods so it leads to the conclusion that they will periodically (pun unavoidable) be indisposed.

No heavy math required, said period being 28 days.

Right, for this particular case the math is simply overkill. In the general case, autocorrelation is a reasonable simple method to determine the periodicity of a time-series.

Yeah, that's the better way to go and might be what they did. Wish I could find that paper now.

But I still thought it was a nice example to illustrate frequencies and periodicity in a non-wave example.

There is a camp of economists who enjoy applying math which is far too complicated for the situation. It's great fun.

How would you quantify this effect without using fourier transforms/autocorrelation?