Time series harmonic check

[gver]

hi.. if i am given a time series is there a way to check if it is harmonic in nature .. i am assuming that interprets as the time series having a long term mean around which it oscillates ..
let me know if i am interpreting it incorrectly

also, if there is a way then how do we calibrate the long term mean and the reversion speed

Earlier i tried calibrating a mean reverting series to the OU process and solved for params to compute LTM and half life stuff ..

but the idea here is to have something mathematical to gauge first if something is reverting and then perhaps use something easier or more intuitive for LTM and reversion speed

apologies for the verbose post .. way too much sleepy !

 

[yetanotherquant]

Likely, you wants to check the stationarity.
There are some statistical tests for it, just google.

Sometimes you can transform the initial time series to the stationary one (e.g. by taking log() of diff() of it).

And yes, stationary time series can be represented in frequency (fourier) domain.
There is, however, a larger class of locally-stationary time series (whose spectral parameter do change in time, however, relatively slowly).

You may have a look how I applied them to the analysis of volatility regimes
http://yetanotherquant.com/stockmarket/vola_wavelet.pdf

Generally, plotting the wavelet spectra helps you (visually) judge whether the time series is stationary or not.

 

[yetanotherquant]

Here are the wavelet spectra vs. (smoothed) Fourier periodogram.
In wavelet spectra one sees that there is a (dis)appearing periodicity between level 8 and 10

 

[gver]

thanks a lot ! .. will check this out