[Rd] Max likelihood arima code question

Joseph Yarmus joseph.yarmus at oracle.com
Tue May 17 00:17:49 CEST 2005

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."

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