Calculating autocorrelation on time series data

Hi,

I am extremely new to matlab. For part of my research work I urgently need to calculate the autocorrelation values for time series data which are in the following form.

 time(femtoseconds)            distance (Angstrom)

        0                      15.769
      100                      16.160
      200                      15.571
      300                      15.816
      400                      15.702
   ......                      ......
   ......                      ......
    49990                      15.907 

    I want to calculate the autocorrelation for these distance data points which have been obtained at 100 femtosecond intervals (there are 5000 distance points).

   Assuming that I am a beginner to matlab could anyone of you suggest a way to calculate the autocorrelation for these time-series distance data using matlab?
I really appreciate this help.

Thank you

Sajeewa Dewage

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/29922-why-your-question-is-not-urgent-or-an-emergency

Answer 1

[Wayne King]

If you have the Signal Processing Toolbox, you can use xcorr() to find the autocorrelation sequence.

If you have the Econometrics Toolbox, there is an autocorr function.

[Sajeewa]

Hi Wayne,

Thank you very much for the quick reply. I am having difficulty in figuring out what nLags, M and nSTDs mean with respect to my data above to implement the autocorr function.

The 'series' attribute of autocorr refers to the set of distance values.

I looked up the definition of the function autocorr at http://www.mathworks.com/help/econ/autocorr.html but the definitions of nLags, M and nSTDs seem too abstract for me. Could you please explain the meanings of those three attributes in simpler terms with respect to my problem. I would really appreciate that.

Thank you

Sajeewa

[Sajeewa]

Hi Wayne,

As I have 5000 data points, the value of nLags is 4999.

But in deciding M, the I can safely assume that the system would be relaxed (autocorrelation is lost)after 4000 steps. So in that sense would my value of M be 4000? (that is what I understand from the definitions given in Matlab for the attribute definitions)

I guess the two standard deviations would be good enough, so my nSTDs would be 2 (which is the default).

I am still uncertain about the value of 4000 for M. If I overestimate M, would it affect the resultant correlation values a lot?

Thank you

Sajeewa

[Wayne King]

Do you want to use autocorr() or xcorr()? Please answer that question first. Please confirm which toolboxes you have installed and which function you prefer to use.

Answer 2

[Youssef Khmou]

hi Sajeewa,

 try :

 c=xcorr(distance,'biased'); % biased estimate

[Sajeewa]

Hi Youssef,

The autocorrelation values calculated in the above way are not between 0 and 1. What I really want to do is to plot the autocorrelation function against time and then find the time at which the value of autocorrelation goes from 1 to 0. Could you please advise me as to how to achieve this? I really appreciate your help.

Thank you

Sajeewa