Can we identify ARIMA($p,d,q$) model without looking at the ACF and PACF plots?
I am trying to write a generalized R programme for fitting time series models.

We may find out the orders $p$, $d$ and $q$ from the ACF and PACF plots, but I want to know how to identify them from the numerical values of the ACF and PACF.

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    $\begingroup$ You can use any number of criteria to choose the model... but there are already R programs for choosing the order of ARIMA. $\endgroup$ – Glen_b Feb 2 '16 at 6:27
  • $\begingroup$ No need for re-designing the wheel, it already exists in R, check auto.arima function in forecast library, cf. otexts.org/fpp/8/7 $\endgroup$ – Tim Feb 2 '16 at 12:31
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    $\begingroup$ Thanks Tim for your response, I tried this function in forecast package But auto.arima not gives the exact order of our data which is used for forecast. From ACF and PACF plot i found the ARIMA order and is used for future forecasting.But i want to know to find ARIMA order through programmatically in R. $\endgroup$ – Shahnawaz Feb 3 '16 at 5:09

The common approach is to choose the model that minimizes the AIC, the BIC or a modified version of these criteria.

Section 3 in this paper $^{[1]}$ mentions some software tools that implement automatic detection procedures for choosing an ARIMA model. You may find more details in the documentation or reference papers.

[1] Rob J. Hyndman, Yeasmin Khandakar (2008). Automatic Time Series Forecasting: The forecast Package for R. Journal of Statistical Software. DOI: 10.18637/jss.v027.i03.

  • $\begingroup$ we are plotting acf and pacf plot in r using acf and pacf function and it generate plot to identified that our data is stationary or not and also used for finding ARIMA order.but i want to generalise my code using acf and pacf value . $\endgroup$ – Shahnawaz Feb 23 '16 at 11:12
  • $\begingroup$ this is the example :-> acf<-acf(ATM_RC052009_CHAROLI_TS) > > acf Autocorrelations of series ‘ATM_RC052009_CHAROLI_TS’, by lag 0.00000 0.00274 0.00548 0.00822 0.01096 0.01370 0.01644 0.01918 0.02192 0.02466 0.02740 0.03014 0.03288 0.03562 0.03836 0.04110 0.04384 0.04658 0.04932 0.05205 1.000 0.438 0.313 0.222 0.179 0.065 0.052 0.008 0.111 -0.016 -0.005 -0.081 -0.099 -0.098 -0.200 -0.193 -0.089 -0.111 -0.107 -0.103 0.05479 0.05753 -0.100 -0.084 $\endgroup$ – Shahnawaz Feb 23 '16 at 11:15
  • $\begingroup$ @Shahnawaz I think it is easier to implement a model selection based on the AIC or BIC rather than on the ACF and PACF. I don't know a reasonable design of a procedure that chooses the model looking at the values of the ACF and PACF; I don't think it is the right approach anyway. $\endgroup$ – javlacalle Feb 25 '16 at 19:30
  • $\begingroup$ I would recommend you to read the papers and code of the references I mentioned. It can be an interesting pedagogical exercise where you may come up with some ideas and try some variations or alternatives to the common approach. $\endgroup$ – javlacalle Feb 25 '16 at 19:31
  • $\begingroup$ Thanks javlacalle,Now i got it and it's easier to implement and choosing model based on minimum AIC and BIC value. $\endgroup$ – Shahnawaz Feb 29 '16 at 6:03

No, you can't identify the model just from the ACF and PACF. You need to also consider looking at outliers, changes in level/trend/seasonality/parameters/variance. If you assume that these don't exist and try and force a model to the data you are prone to model specification bias.

Tsay, R.S. (1986). "Time Series Model Specification in the Presence of Outliers," Journal of the American Statistical Society, Vol. 81, pp. 132-141.



  • $\begingroup$ ok i will chk and read that paper and let u know $\endgroup$ – Shahnawaz Feb 3 '16 at 16:30
  • $\begingroup$ You might need to also read these en.wikipedia.org/wiki/Chow_test ww.unc.edu/~jbhill/tsay.pdf www.jstor.org/stable/1391308 No link for the change in trend or seasonality as that is proprietary to Autobox. $\endgroup$ – Tom Reilly Feb 3 '16 at 18:21

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