Most people seem to argue that lag plots and autocorrelation plots are useful for determining whether some univariate time series data is random or not.

I feel like I could accomplish this task by just plotting the time series normally. I don't see the point of a lag plot or a autocorrelation plot, plotting the raw time series seems to give a good enough intuition of the behaviour of the function.

Can someone enlighten me on the true usage of lag and autocorrelation plots?


1 Answer 1


There are two major advantages to making a lag autocorrelation plot

1) You get to see the number of significant lags of autocorrelation. This can not often be established just by looking at a time plot.

2) You get to estimate the lag autocorrelation, which indicates the strength of the correlation.

Aside from these two advantages, the point of statistical analysis is to summarize raw data with numerical quantities so as to abstract the noise from the signals. When data is tirelessly huge, naked eye analysis fails in addressing both the above points.

Below is an example of when naked eye analysis cannot help you differentiate between two time series plots, but an ACF plot helps.

Two different time series look very similar, but lead to different autocorrelation plots.

  • $\begingroup$ Hm, thanks for the answer - but, if I zoomed in on a certain part of the series, I could probabily determine that they are correlated. What should invoke someone to use a autocorrelation plot? "Hey, I want to see if my signal can be predicted by itself?" $\endgroup$
    – user46925
    Commented Mar 18, 2016 at 18:44
  • $\begingroup$ And would you be able to zoom into every possible frame for a sample size of $10^6$? Would you be able to quantify whether your conclusion is statistically valid or not? Would you be able to determine how many lags of correlated do you have? If data are not inherently time dependent (or dependent) there is generally no reason to look at ACF plots. But if the data are time dependent, ACF or PACF plots give statistical insights to the correlation, as opposed to heuristic insights. $\endgroup$ Commented Mar 18, 2016 at 18:46
  • $\begingroup$ If there wasn't a lot of data, I could. I suppose this graphical device is only useful in large datasets. $\endgroup$
    – user46925
    Commented Mar 18, 2016 at 18:48
  • $\begingroup$ Sure, you could say that the data seems dependent, but how would you quantify the data? Would you be able to say how many significant lags there were? In addition, the ACF plots summarize all of the data, and not just parts of the data. $\endgroup$ Commented Mar 18, 2016 at 18:52
  • $\begingroup$ Just to clarify, a signficant lag is a lag with a 'bump'? $\endgroup$
    – user46925
    Commented Mar 18, 2016 at 18:55

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