Can we identify ARIMA model without looking at ACF and PACF plot? 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.
 A: 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.
A: 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.  
http://www.orms-today.org/orms-6-08/survey.html
http://www.autobox.com/cms/index.php/products/autobox/text-references
