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I am new to time series analysis, I have come across ACF and PACF while working on time series data set. There is a confusion, in some links/texts ACF and PACF is plotted without taking difference i.e. time series is non-stationary and they just mention that depending upon shape of ACF and PACF we can decide if we need to make time series stationary or not?

There are links/texts which mention that in order to decide AR or MA or ARMA model, plot ACF and PACF after taking difference of series.

Does this mean that ACF and PACF can be plotted for both non-stationary and stationary series? but purpose is different.

For non-stationary time series, PACF and ACF plots can be used to visualize if time series is stationary or not

For stationary time series PACF and ACF plots can be used to determine the model and its order.

Is my understanding correct?

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  • $\begingroup$ There’s a similar question/answer here. ACF/PACF can be useful both before and after differencing. $\endgroup$
    – joshualeond
    Commented Aug 29, 2022 at 0:43

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Generally speaking, ACF and PACF help you to find out which ARIMA type best suits your data (eg ARIMA(2,1,1)). The time series has to be stationary when checking ACF and PACF. https://towardsdatascience.com/identifying-ar-and-ma-terms-using-acf-and-pacf-plots-in-time-series-forecasting-ccb9fd073db8 maybe here you can find some further clarifications. It is important to point out that many times there isn't a clear answer by just looking at ACFs and PACFs, so you can use tools implemented in almost all statistical softwares to find out which ARIMA type best suits your data.

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  • $\begingroup$ But when i plot ACF and PACF on stationary data it looks stationary and all values are within 95% CLs $\endgroup$
    – Brekhnaa
    Commented Dec 24, 2020 at 4:33
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To your questions in order:

  • Yes, ACF and PACF can be plotted for both stationary and non-stationary time series data.

  • Yes, to me your understandings for the different purposes are correct.

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    Commented Apr 20 at 23:41

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