A researcher is trying to determine the appropriate order of an ARMA model to describe some actual data, with 200 observations available.

She has the following figures for the log of the estimated residual variance (i.e. log ( ˆ σ2)) for various candidate models. She has assumed that an order greater than (3,3) should not be necessary to model the dynamics of the data. What is the ‘optimal’ model order?

ARMA(p,q) log( ˆ σ2)

model order

(0,0) 0.932

(1,0) 0.864

(0,1) 0.902

(1,1) 0.836

(2,1) 0.801

(1,2) 0.821

(2,2) 0.789

(3,2) 0.773

(2,3) 0.782

(3,3) 0.764 AppendixLO1