enter image description hereI've been fitting ARMA-GARCH models in R and I've found that when I plot the ACF and PACF of the model residuals, the lags ($x$ axis) go up to and beyond two million. What does this mean? Is it wrong? Also, can one ignore lags that are 'just' above the significance level?

Edit: Here is the acf and pacf plots I'm talking about. Notice the scale of the x axis ...

  • $\begingroup$ Millions on the $x$ axis could be due to scale of the axis. If you have yearly observations, while the axis is in seconds, you will have millions there. I suppose you do not have millions of ACF values, but just a few (or a few dozen) of ACF values on a scale with millions. (Posting a graph would help.) $\endgroup$ Nov 19, 2015 at 15:40
  • $\begingroup$ I have 2100 observations but i haven't specified any time frame. I'm just using the data as a vector (in R). Can I still use those ACF and PACF plots as normal? Like, if there are no significant values can I assume the residuals are white noise? $\endgroup$
    – James
    Nov 19, 2015 at 16:47
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    $\begingroup$ If you really had 2 million ACF lags, even at 200 separate values per centimeter (which would be very hard to distinguish visually even if your display medium can accurately render it) you'd have a graphic that would be 100 meters wide! My screen is only about the size of (landscape) A4 paper, less than 0.3 m wide. I suspect that you really don't have 2 million separate lags. [On my screen, 20 values per cm is already getting tricky; that would suggest needing a graphic a kilometer wide.] -- beware confusing the labelling on the axis with the actual number of lags $\endgroup$
    – Glen_b
    Nov 20, 2015 at 0:27
  • $\begingroup$ If you show us your data and how it is set up in R all should become clear, so why not tell us? Here is a wild guess. Somehow your data are daily but the times are in seconds. I note that 86400 seconds in a day seems consistent with the number of spikes shown and the lag axis scale. $\endgroup$
    – Nick Cox
    Nov 21, 2015 at 16:35

2 Answers 2


As concerns your first question, I would say that there is something wrong, unless you have billions of data points and the interval between each data point is very small. In any case, autocorrelation in residuals is generally synonym of misspecification in the model.

As for your second question, I would say that 'No', you cannot ignore lags that are just above the significance level. Otherwise, that would not be a significance level...

When ignoring important lags, you acknowledge that the data generating process that you use is statistically different from the true data generating process. Therefore, you introduce misspecification into your model.

Whether you are fine with that or not is completely up to you.


Millions on the $x$ axis could be due to the scale of the axis. If you have yearly observations, while the axis is in seconds, you will have millions there. I suppose you do not have millions of ACF bars, but just a few (or a few dozen) of them -- but on a weird scale.

Posting the actual ACF and PACF plots would be helpful.

To answer the comment: if the only problem is indeed the weird scale of the $x$ axis, i.e. if this is a technical nuisance, you could in principle neglect that. Under no significant ACF or PACF values you may assume your model errors are non-autocorrelated. However, there may be other forms of dependence (e.g. ARCH patterns) in them not revealed by ACF or PACF; hence, you cannot conclude immediately that your model errors are independent.

  • $\begingroup$ How does one post pictures here?? Help...? $\endgroup$
    – James
    Nov 21, 2015 at 5:31
  • $\begingroup$ When editing your post, there are several buttons at the top of the window: boldface, italicized, ..., picture. Try that one. $\endgroup$ Nov 21, 2015 at 6:58

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