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I have a time series that looks like this

enter image description here

I was asked to display the autocorrelation function and perform ADF test and based on that suggest a d for further analysis. I get plots like this and can decide how to choose d,

enter image description here

enter image description here

enter image description here

The ADF test is something like this

    Augmented Dickey-Fuller Test

data:  Yt_diff1
Dickey-Fuller = -3.0757, Lag order = 4, p-value = 0.1312
alternative hypothesis: stationary
Augmented Dickey-Fuller Test


data:  Yt_diff2
Dickey-Fuller = -2.2484, Lag order = 4, p-value = 0.4738
alternative hypothesis: stationary
User1865345
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moon
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  • If this is a purely practical question, try auto.arima() and have it determine the appropriate order of differentiation. – Durden Feb 23 '24 at 18:52
  • I tried, it suggests 2! but I asked to determine ACF and ADF, which is hard for me to interpret from here! I mean what should be my explanations for choosing 2 – moon Feb 23 '24 at 18:56
  • Judging by the plot of the original data, there is no unit root, so differencing will not help get rid of it. But since you are asked to do something specific, that insight might not help much. – Richard Hardy Feb 23 '24 at 20:22

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