Lets say I am given time series plot.

enter image description here

How can I estimate $r_1$ and $r_2$ which are sample correlation? I don't understand how to see correlation from data plot.
I know how to get and use ACF and stuff from the data itself but I am having problem with understanding time series plot.

  • $\begingroup$ Why would you try to eyeball a correlation? What's AFC? $\endgroup$
    – Glen_b
    Mar 24 '15 at 5:48
  • $\begingroup$ It is ACF, AFC was typo. Well, I was told to do eyeball it for problem sets and I was really wondered how it works. I have quite amount of stat courses but I always have hard time understanding the plot and eyeball it. $\endgroup$
    – Kane
    Mar 24 '15 at 22:51

The time series itself is probably not the best way to "eyeball" autocorrelations. A standardized scatter plot with the desired lag between the abcissa (x) and ordinate (y) would do a better job. However, you can imagine the time series plotted with lag=1, lag=2 etc. on the same axes. Then the question is how much the original and the lagged series overlap (for lack of a better term). Your series would probably have slowly decaying autocorrelation since there are relatively flat intervals which, after a shifting, still overlap as long as the shift isn't too large. Then it would spike at lag=7 and lag=14 since there is a clear cyclical pattern of 7 days.

  • $\begingroup$ +1. Agreed with the main idea. The overall weekly pattern, although detectable, is also smudged out a bit: the vertical lines are for Thursdays and each was a weekly peak in only about half of the weeks. The overall trend will reduce the damping a bit. $\endgroup$
    – Nick Cox
    Mar 25 '15 at 19:42

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