If the series is non-stationary difference it once and test for stationarity. If it is stationary obtain the correlogram and fit an ARMA(p, q) model to the difference where p is the cut-off point to the PACF and q is the cut-off point to the ACF. This is an ARIMA(p,1,q) model to the original series. If however the difference is still not stationary obtain another difference, and let the process continue.

Hi Ette Etuk

When I performed Augmented Dickey–Fuller test, it gave significant p-value (0.03) so I considered difference as 0 (d=0). So I guess it would be ARIMA (p,0,q) model, would you please suggest if this is how I proceed?

With respect to (d=0), ACF and PACF plots are generated, but I am stuck in selecting the p and q value from the above plots.

Thanks

If d=0, from your plots p=1 the cut-off point for PACF and q=3, the cut-off point for ACF so your model is ARIMA(1, 0, 3) or ARMA(1, 3).

Ette Etuk and Fethiye Burcu Türkmen - Ceylan

Thank you for your suggestions !

If your series is stationary at level, choice of ARIMA is not appropriate.

I totally agree with Prof Ette Etuk . The partial autocorrelation at lag k is often 'equal to the estimated AR(p=k) coefficient in an autoregressive model with k terms'. If our PACF plot has a significant spike only at lag 1, meaning that all the higher-order autocorrelations are effectively explained by the lag-1 autocorrelation. There you have your two choices, ARIMA(p=1,d=0, q=3) or ARMA(1,3). Perhabs, try also ARMA(1,1), ARMA(1,2) and make selection for parsimonious model the usual way, ie., AICc. You can complement the regression model (after the parameters have been obtained ) either ljung box Q test or Durbin-Watson's, be sure there wasn't mispecification.

Here is a rule I got: "Rule 7: If the ACF of the differenced series displays a sharp cutoff and/or the lag-1 autocorrelation is negative(i.e., if the series appears slightly "overdifferenced")then consider adding an MA term to the model. The lag at which the ACF cuts off (say l) is the indicated number of MA terms, q=l" from https://people.duke.edu/~rnau/411arim3.htm .

No concesus, but generally, what most people tend to do, is eyeball using PACF and ACF visualizations. *This is really an important question, Akshay Ware .

Best wishes Ibiloye A. C.

Thank You Abiodun Christian Ibiloye , for the detailed explanation.

i am doing forecasting using arima, and i have similar plots but my model is giving flat line forecast in alteryx. also how do you know what is your d ?