Thanks for your reply Elman Sir. I am studying a process where DNA is fluctuating between B-DNA and A-DNA states (only 2 states). this transition for a given molecule can occur below thermal fluctuations and hence this to and fro transition between B and A states is occurring repeatedly over a time.

So, I feel due to this reason it will never decay to zero. is this expected in such process?

If I want to calculate timescale for a process using exponential fit, is it correct to fit equation to the initial part of decay where it touches zero first time?

Thanks for the suggestion Elman Sir. 

Thanks for the suggestion on cross-correlation calculation. After your second suggestion, I found this recent publication in J. Phys. Chem. B (DOI: 10.1021/acs.jpcb.5b06217) which is very similar to what I intended to do. Authors in this paper also used cross and auto correlation to study dynamics of DNA structural parameters.

Please, can you suggest me any literature to understand one more aspect. What simple analysis can I perform on time series data to check any presence of nonlinear dynamics?

I will work on the problem and will reply back. Thanks for the suggestions. 

Hello Mandar,

Those "peaks" at about 2500 and 6400 ps suggest some "periodicity" in your time-series, i.e., oscillating processes with periods lengths at approx. those values.  If you were to do a spectral analysis (essentially a Fourier Transform) of your time-series, you would expect to find peak amplitudes at frequencies corresponding to those particular periods.  

Note that such a transform is purely linear - to test for nonlinearity, try the "BDS test" statistic (after Brock, Dechert, and Scheinkman - e.g., Brock, W.A., W.D. Dechert, J.A. Scheinkman and B. LeBaron (1996). “A Test for Independence Based on the Correlation

Dimension”, Econometric Reviews, 15, 197-235).  This is based on correlation integrals, and estimates the likelihood that any can 2 time-series remain "close" to each other over some time interval - if they do, then the dynamics are probably  linear.  Better to google for the details of BDS and other related tests than to go into them here...!

Regards,

Enda

It looks like there's some kind of cyclical pattern... the signal is strongly related to the previous value, the correlation decreases as time passes by... but it also seems correlated to the vaslues (approximately) T-3000, T-6000 and T-9000 ...