firstly I would like to say that I'm newbie here, so hi everyone, and please be patient if I do something wrong. And sorry for my level of used english, hope everything will be clear

Now, I have a problem with "comparison" of two time series (TS): measured observations and generated TS. I would like to decide whether the second TS is statistically "relevant, similar" to the first one so that the first TS can be replaced by the second TS. Can anyone help me?

I can say now that most of the descriptive characteristics are similar (means, standard deviations, higher moments like skewness, kurtosis; quantiles etc.), but I think that is not enough, say, because of some difficulties may occur since I have to deal with bimodal distributions, but maybe not..

So what kind of analysis should be performed? My friend advised me to look at autocorrelation functions, cross-correlation, coherence, psd and similar techniques, but I am not familiar with them.

I'm using Matlab, and if any figure is needed, I immediately post it.

Any help is appreciated.

Thanks, Jan.