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I am dealing with OLS regression using Time-series data. After having the regression result I plot the residual correlogram in order to see if there is autocorrelation. Here appears that there is significance in the lag 3. However, no clear pattern is shown and the significance of the lag 3 is of order at 10%. Does this mean that I should use another time-series regression model? If that is the case, someone could tell me which one should I use?

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The ACF and PACF that you plotted seems me to show uncorrelated residuals. From this seems that your specification is acceptable. The fact that the 3rd lag appear significant different from 0 at 10% level is not strange. Even if your residuals come from iid normal draw it can happen easily by chance. Some autocorrelation test as Ljung Box (see here https://en.wikipedia.org/wiki/Ljung%E2%80%93Box_test) can give you a formal response.

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  • $\begingroup$ Thank you very much for the reply. Could you tell me how many lags do I have to put to test for the Ljung Box test? I have tested for 12 lags and the p-value appears 0,319. The Q' values is 13.7139 and the Chi-square 21,026. I am correct if I say that the null hypothesis of no autocorrelation can't be rejected since the p-value is higher than 0,05? $\endgroup$ Commented May 4, 2020 at 16:09
  • $\begingroup$ Your interpretation is correct and it confirm my guess. You are right, number of lags matters. I don't remember if some rule of thumb exist for choose them. What important is that, as in your case, “strange correlation” that appear in correlograms are considered. To consider the same lags that you plotted can be an idea. If you consider useful my answer and comments, you can “upvote” it. Moreover, if it is your favourite you can accept it. $\endgroup$
    – markowitz
    Commented May 4, 2020 at 17:03

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