On the Order Determination of ARIMA Models

deciding the order of an ARIMA (autoregressive integrated
moving average) model is discussed. The possibility of removing this difficulty by using
the MAICE (minimum AIC estimation) procedure, which selects a model by using
Akaike's Information Criterion (AIC), is checked with the numerical examples treated
in the book by Box and Jenkins.
Keywords : ARIMA MODELS; BOX-JENKINS PROCEDURE; AKAIKE'S INFORMATION CRITERION ;
MAXIMUM LIKELIHOOD ESTIMATION
1. INTRODUCTION
APPLYINGthe Box-Jenkins (B-J) procedure described in Box and Jenkins (1970), Cha~eld
and Prothero (1973) and Newbold and Granger (1974) pointed out the difficulty of distinguishing
between different autoregressive moving average models on the basis of the observed
data. Kendall(1971) also pointed out the difficulty in choosing a model when several models
fit the data equally well. This indicates the inherent difficulty at the identification stage of the
procedure of choosing the order of the model.
It was suggested by Priestley (1974), in the discussion of the paper by Newbold and Granger
(1974), that the new procedure of order determination developed by Akaike (1972a and
1973a), might be a promising one. Akaike's Information Criterion (AIC)is defined as follows:
AIC =(- 2) log, (maximum likelihood) +2 (number of free parameters).