ACF plot in ARIMA



I have run ARIMA in R.I am receiving ACF and PACF plots attached.Please guide as to the order which they suggest.Also whether series seems to be stationary?After running adf test p value comes out to be 0.01 on original series…


Hi @nehak

First of all, you cannot fit an ARIMA model on a time series until and unless you are sure that the series is stationary. A time series is stationary if its mean level and variance stay steady over time. You can start with a graphical plot of your original series to check whether it is stationary (trend around the mean indicates that it is stationary whereas an increasing trend indicates that it is non-stationary). Then you can check the ACF & PACF plots of the original series. If the lags of the ACF series die out very slowly whereas the lags of the PACF series dies out quickly, then the series is most likely non-stationary. If both the graphs have a few significant lags that die out quickly, then the series is most likely stationary.

Other tests to check stationarity:

  • The Ljung-Box test examines whether there is significant evidence for non-zero correlations at lags 1-20. Small p-values (i.e., less than 0.05) suggest that the series is stationary.

  • The Augmented Dickey–Fuller (ADF) t-statistic test: small p-values suggest the data is stationary (In your case, a p-value of 0.01 indicates that the series is stationary).

  • The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test: higher p-values (i.e., greater than 0.05) suggest that the series is stationary.

For a detailed explanation to check stationarity in a time series using ADF test, you may refer to this post.

Hope this helps.



@debarati_dutta8 and @nehak , after looking at the ACF plot, dont you think that the data does not seem to be stationary

I know that the Dickey Fuller statistic says so



@nehak @anantguptadbl : I generally apply three tests (adf,pp and kpss) to see whether a series is stationary or not. It is always suggestible to go with KPSS test when compared to ADF and PP test when you are having contradictory inference from the three.
As in this case, where adf is suggesting the series is stationary(though it is not), better go with KPSS test


Hi @sowmiyanm, Is there any logic behind this, I mean theoretically



If you see the null hypothesis for all three tests
i) Adf test , Ho is a Unit root
ii) PP test, Ho is a Unit root
iii)KPSS test, Ho is stationarity

Here KPSS is a test for stationary, whereas the other two are tests for Unit root. Unit root tests have low power i.e sometimes these tests are not able to distinguish between values near to 1 (say 0.95), thus giving contradictory results.