Having the following CCF from the residuals of 2 modelled series, which lags should be taken into account to explain how positively or negatively $x_t$ and $y_t$ are correlated?

enter image description here

Zoom out enter image description here


Generally you want to look at lags that are significant statistically. So, I'm not sure what the blue lines are but if they are confidence intervals for a zero acf value, then look at lags that cross those lines. Note though that the calculation of the ccf ( particular those related to returns in finance ) can often be quite unstable. Therefore, you should look at different time frames and see if the same ( or atleast similar ) lags keep being signifcant.

Also, what does the second plot represent ?

  • $\begingroup$ Thank you for answering. The second plot is the same ccf but with lag.max=250 instead of lag.max=12 as in the first plot. In the case lag.max=250, there are more positive lags crossing blue lines than negative. Therefore my question is about if having a total of 400 observations which lag.max I have to evaluate. See that in the first plot there aren't enough positive lags to say that $x_t$ is positively correlated to $y_t$ as in the second, which come from the same ccf. $\endgroup$ – fina May 5 '19 at 8:58
  • 1
    $\begingroup$ Hi: You're welcome. definitely don't use lag.max = 250. there are only 400 observations so there won't be enough degrees of freedom for that many lags. with 400 observations, a lag max of 12 is much more reasonable. $\endgroup$ – mlofton May 5 '19 at 14:09
  • $\begingroup$ Thank you. So, lags must be equal to the stational period? -In this case 37 years 456 observations by 12 groups of 37. $\endgroup$ – fina May 5 '19 at 14:13
  • $\begingroup$ No, they don't have to be equal. the idea is that, when the ccf is calculated, for any lag value, lag*, it uses a subset of the observations where the lag is lag*, in order to calculate the correlation at lag*. So, if you try to calculate an estimate of the correlation at lag 250 and you only have 400 observations, you have less and less ( pairs of ) observations that have a lag of 250 so you're denominator in the calculation for that lag* will be smaller say that if you're calculating the corr at lag 3 say. $\endgroup$ – mlofton May 6 '19 at 16:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.