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I have a non-stationary dataset which shows the prices. I wanted to apply time series analysis on it. I took the first differences of the dataset and it became stationary. Then I determined the p and q values by looking the ACF and PACF plots. However, I was a bit confused because I saw that many people applied Box-Cox transformation on their non-stationary dataset and took the differenced of these datasets until they reach a stationary series.

My question is arising here. Should I work with Box-Cox transformed data first? Why some people are working with the differenced series when others are working with Box-Cox transformed series?

Thanks in advance.

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1 Answer 1

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Box-Cox transformations are variance stabilizing transformations, whereas differencing are mean stabilizing transformations. In plot 2 below you see the series in plot 1 with its variable stabilized by a Box-Cox transformation. In plot 3 you see plot 2 with its mean stabilized by first-differencing.

original<-AirPassengers
bc<-BoxCox(original,BoxCox.lambda(original))
fd_bc<-diff(bc)

par(mfrow=c(3,1),mar=c(3,5,1,1))
plot(original)
plot(bc)
plot(fd_bc)

enter image description here

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  • $\begingroup$ Thank you for your answer! $\endgroup$
    – iloloa
    Nov 15, 2021 at 9:01
  • $\begingroup$ @iloloa: you're welcome. Don't forget to click to mark this question as answered. $\endgroup$ Nov 15, 2021 at 9:28
  • $\begingroup$ I need at least 15 reputation to cast a vote, but I voted :) $\endgroup$
    – iloloa
    Nov 17, 2021 at 16:15
  • $\begingroup$ For voting you need min 15 reputation but for marking the question as answered, you don't. 😃 $\endgroup$ Nov 17, 2021 at 19:28

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