FindingAn appropriate valuesvalue of ''p'' and ''q'' in the ARMA(''p'', ''q'') model can be facilitatedfound by plotting the [[partial autocorrelation function]]s. for an estimate ofSimilarly, ''pq'',andcan likewisebe estimated by using the [[autocorrelation function]]s. forBoth an''p'' estimate ofand ''q''. Extended autocorrelation functions (EACF) can be used todetermined simultaneously determineusing pextended andautocorrelation qfunctions (EACF).<ref>{{Cite web|last=Missouri State University|title=Model Specification, Time Series Analysis|url=http://people.missouristate.edu/songfengzheng/Teaching/MTH548/Time%20Series-ch06.pdf}}</ref> Further information can be gleaned by considering the same functions for the residuals of a model fitted with an initial selection of ''p'' and ''q''.
Brockwell & Davis recommend using [[Akaike information criterion]] (AIC) for finding ''p'' and ''q''.<ref>{{cite book |last1=Brockwell |first1=P. J. |last2=Davis |first2=R. A. |title=Time Series: Theory and Methods |edition=2nd |publisher=Springer |___location=New York |year=2009 |page=273 |isbn=9781441903198 }}</ref> Another possible choice for order determiningoption is the [[Bayesian information criterion|BIC]] criterion(BIC).
===Estimating coefficients===
ARMA models in general can be, afterAfter choosing ''p'' and ''q,'', ARMA models can be fitted by [[least squares]] regression to find the values of the parameters which minimize the error term. It is generally considered good practice to find the smallest values of ''p'' and ''q'' which provide an acceptable fit to the data. For a pure AR model, the [[AR model#Calculation of the AR parameters|Yule-Walker equations]] may be used to provide a fit.
ARMA outputs are used primarily to forecast (predict), and not to infer causation as in other areas of econometrics and regression methods such as OLS and 2SLS.
Unlike other methods of regression (i.e. OLS, 2SLS, etc.) often employed in econometric analysis, ARMA model outputs are used primarily for the cases of forecasting time-series data. Their coefficients are then as such only utilized for prediction. Other areas of econometrics look at the causal inference, time-series forecasting using ARMA is not. The coefficients should then only be seen as useful for predictive modelling.
