[Rd] Max likelihood arima code question

Joseph Yarmus
Tue, 17 May 2005 00:18:00 -0000

The documentation for arima indicates that the stabilization of the AR
parameters takes place during optimization while the MA terms are
constrained afterwards. We were curious as to why that was done. How
does this affect the Kalman recursion given that Jones states that both
stability and invertibility are required? Is this a performance trick?

Please respond directly to me as I am not a member of the list. Thanks!

-joe yarmus

 From the R arima doc:
"If transform.pars is true, the optimization is done using an
alternative parametrization which is a variation on that suggested by
Jones (1980) and ensures that the model is stationary. For an AR(p)
model the parametrization is via the inverse tanh of the partial
autocorrelations: the same procedure is applied (separately) to the AR
and seasonal AR terms. The MA terms are not constrained to be invertible
during optimization, but they will be converted to invertible form after
optimization if transform.pars is true."