Typically "frequency" means the same thing: something that is repeated over time. I'll mention a specific economic example I've seen (sorry, can't recall exactly where) to illustrate.
Economists wanted to explain a productivity gap between male and female employees at some employer. So after looking at the Fourier transform of timeseries of sick days, they noticed that men's sick days behaved like a bump function near 0. Essentially, if you are sick today, this increases the odds of him being sick tomorrow.
On the other hand, the Fourier transform of women's sick days had spikes at f=1/28 days as well as the bump at 0. This means if a woman is sick today, the odds are increased that she will be sick n x 28 days from now (n an integer).
That's what the Fourier transform does: if your signal has a component which repeats over time, the Fourier transform will find it.
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.
Economists wanted to explain a productivity gap between male and female employees at some employer. So after looking at the Fourier transform of timeseries of sick days, they noticed that men's sick days behaved like a bump function near 0. Essentially, if you are sick today, this increases the odds of him being sick tomorrow.
On the other hand, the Fourier transform of women's sick days had spikes at f=1/28 days as well as the bump at 0. This means if a woman is sick today, the odds are increased that she will be sick n x 28 days from now (n an integer).
That's what the Fourier transform does: if your signal has a component which repeats over time, the Fourier transform will find it.