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I ran various diagnostic tests on a time series dataset using R. The null hypothesis for non-stationarity was not rejected using the Dickey-Fuller test, and moreover the null hypothesis for the Ljung-Box test was not rejected either; implying residuals follow a random pattern.

When I run the acf and pacf plots, the acf gradually decreases while pacf cuts off sharply after the first lag. However, when I run auto.arima the model is specified as (0, 1, 0) - random walk with drift.

Am I right in saying that the ARIMA calculation conflicts the findings of acf/pacf, since the acf/pacf result implies an AR(1) process?

I would appreciate any advice as to how I should proceed from here, or what weight I should give to the various results in my interpretation.

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  • $\begingroup$ Post your data. $\endgroup$ – Tom Reilly Mar 31 '16 at 18:09
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  • ACF/PACF indicate AR(1)
  • Dickey-Fuller indicates a unit root

Hence, both taken together indicate an AR(1) with a unit root, another name for which is a random walk.

  • auto.arima selects random walk with drift

This is quite in line with the above except perhaps for the drift. However, depending on the specification of the (presumably augmented) Dickey-Fuller test, you might have a drift there. In sum, there is no clear evidence of conflict between {ACF/PACF and Dieky-Fuller} and the model selected by auto.arima.

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