QUESTION: 

From - Thu Dec 11 06:12:17 1997 Newsgroups: sci.stat.math Subject: Re: identify the ARIMA model's parameters Date: Wed, 10 Dec 1997 17:20:54 -0500 To: bickel a0572@mail.kscgeb.edu.tw Xref: Supernews70 sci.stat.math:16084 bickel wrote: I have a question about the ARIMA model : when use ARIMA, we must decide the parameters: p, d, q if someone can tell me how to identify the p, d, and q except for using ACF function and PACF function. please tell me method or introduce some books or other tool. Thank you very much!

ANSWER: 

If I understand your question, you don't want to use ACF and PACF to identify the pdq structure. If that is your question, then you could try using the unconditional and conditional regression coefficients. For example, just compute the regression between Y and Y lag and list these regression coefficients for lag 1 to k. These are unconditional regression coefficients or unconditional correlation coefficients. Now compute a multiple regression between Y AND Y (LAG1) AND Y(LAG2 ). The conditional regression coefficient for the second input, i.e. Y (LAG2) will tell you how important LAG2 is in predicting Y. Now you compute a multiple regression with three input series Y(LAG1), Y(LAG2) and Y(LAG3) and evaluate the significance of the conditional correlation associated with Y(LAG3). This will tell you how important LAG3 is and so on. Eventually if there are more significant simple correlations than conditional correlations you declare the model to be an AR model. The number of coefficients (p) would be equal to the number of significant conditional correlations. In a similar manner, if there are more significant conditional correlations than simple correlations you would declare the model to be a MA model. The number of MA coefficients would be equal to the number of simple correlations that were deemed to be significant. The d in the model is just a particular case of AR terms and is normally evidenced by a strong set of simple regression coefficients that slowly decay in absolute value. Of course some readers will see that this approach of using simple regression coefficients and conditional regression coefficients is exactly what the ACF and the PACF are. To some extent it might have been preferable for Box and Jenkins, and others, to couch their model identification schemes in terms of regression coefficients and never to have mentioned ACF and PACF at all. For a list of books on the subject see http://www.autobox.com/referenc.html for software that does this automatically, even in the presence of outliers, seasonal pulses, level shifts and local time trends see http://www.autobox.com for more educational stuff see http://www.autobox.com/teach.html for human help call 215-675-0652 and we will try and help more. Good luck. P.S. The whole area of ARIMA identification requires robust procedures which in plain English means outlier identification techniques, variance change techniques and parameter change detection procedures all of which are in AUTOBOX.