Meaning of a lag in time-series and autocorrelation

Hi everyone,

I know this might be a very naive question, but I am very new to time series analysis and all of a sudden I have been forced to understand a lot of unfamilair stuff

My first question is "what is the meaning of a lag (how do you define) in time-series data?"

My second question is,

I have a series of data like below

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 find the time at which the distance data is NOT correlated to itself (I guess that is what they call as data being "stationary"). Could anyone of you please tell me how to find that point in time using Matlab?

Thank you very much

Sajeewa Dewage

Answer 1

[Image Analyst]

I guess you'd call xcorr() and plot it and see when the plot "levels out". Did you try that?

[Sajeewa]

Hi Image Analyst,

Yes I tried both xcorr(distance) and xcorr(distance,'biased') both of them produce 10000 points (I have 5000 distances). There is a linear increase from near zero to a huge value (which occurs at 5000th time point) and a symmetric linear decrease back to zero at 10000th point. The whole graph is an isosceles triangle. I don't know what I should make out of this. Does this mean that the whole data set does not acheive stationarity at any point?

Thank you

Sajeewa Dewage

[Image Analyst]

Of course it's going to be twice as long. That's what you expect. If you don't know why, then review how correlation works. If it looks like an isosceles triangle, then your data is just uniform, because the correlation of a box with a box is a triangle.

[Malcolm Lidierth]

This is what you might expect. The correlation at lag=0 is always perfect [the correlation of x(t) vs x(t)]. Try using the 'coeff' option in xcorr.