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I'm still a novice with time series so I'm sorry if this is a little basic.When performing an Augmented Dickey Fuller test on my data I found that lag values from 1-4 all lead me to reject the null hypothesis. Since this is the case, how should I determine the number of lags to use?

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You typically use the longest lag that is statistically significant. You can do that easily by using an ACF graph and looking at any column that crosses through the confidence interval lines denoting statistical significance of autocorrelation given a specific lag. Of course don't test for any more lags than the frequency of your data calls for. If you have quarterly data, test up to 4 lags. If you have monthly data test up to 12 lags.

If the ADF test comes up with a high tau value and a resulting low p-value, you can reject the null hypothesis that the variable is non-stationary. In plain English, in such a situation your variable is deemed stationary (because you reject the null hypothesis that the variable is non-stationary).

In your specific situation, if you have quarterly data and you tested up to 4 lags, you are good. The ADF test has demonstrated that your variable is stationary. If you have monthly data, you may have to use more lags if the longest lag that has a statistically significant autocorrelation is longer than 4. Very often the lag 12 mth has stat. sign. autocorrelation because of seasonality. In that case you should use lag 12 within your ADF test.

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  • $\begingroup$ Thank you for the reply. My data is actually annual, but since each of the 4 lags had a p-value < .05 they should all be included right? $\endgroup$ – Michael Howell Jul 25 '19 at 0:24
  • $\begingroup$ No, I don't think so. Since you are dealing with annual data, from a seasonality and autocorrelation standpoint, only the first lag has true and independent meaning. The other lags (greater than 1) are just a function of the strength of the first lag. So, use ADF with just 1 lag. Your ADF test comes out with a high Tau stat and low p-value. So, you can reject the null hypothesis that this variable is non-stationary. You are in good shape. $\endgroup$ – Sympa Jul 25 '19 at 4:10

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