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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?

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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 ?

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  • $\begingroup$ 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 at 8:58
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    $\begingroup$ 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 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 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 at 16:43

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