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On this website: https://people.duke.edu/~rnau/arimrule.htm I have found information that if the lag-1 autocorrelation is zero or negative, or the autocorrelations are all small and patternless, then the series does not need a higher order of differencing. If the lag-1 autocorrelation is -0.5 or more negative, the series may be overdifferenced. Does lag-1 here refers to the first lag or some "lag minus one"?

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Let the time series be $x_t$, then "lag-1 autocorrelation" is $$\rho(1)=\frac{\operatorname{cov}(x_t,x_{t-1})}{\operatorname{var}(x_t)}$$

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  • $\begingroup$ Could you please tell me whether these time series with the 1st order of difference are already overdifferenced? imgur.com/jsYTpIL With 2nd order difference I get the same results except that the first lag is positive instead of negative. Could you explain what this means? $\endgroup$
    – domke89
    Commented Feb 14, 2021 at 17:13
  • $\begingroup$ Hi @jnan12 it’s better be asked as a separate q. for others to comment as well. $\endgroup$
    – gunes
    Commented Feb 14, 2021 at 21:08

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