shiling99@YAHOO.COM wrote: > David & Dale, > > Thanks for all comments and suggestions.

Always happy to cause headaches. :-)

> Here is the link for ar(1) process > > http://www1.elsevier.com/hes/books/02/04/050/0204050.htm

I get a 'page not found' error. But I believe you. As I said, there's more than one way to represent a given time series.

> and sas online help for sas code. > > Example 20.16: AR(1) Process in ETS.

Yes. And it's almost exactly as I suggested. (BTW, for the person playing along at home, this is example 20.16 in PROC MODEL in the SAS 9.1.3 docs. You'll never find it otherwise.) The SAS doc says to use NPREOBS=20 to get a burn-in, exactly as if you used M=20 in my code. (It's always nice when it turns out the SAS docs back me up. :-)

> In term of small sample, I said in last post "I agree that there is > difference when sample size is small, the initial value becomes not > trivial." > > Using proc arima just want to understand what is the same and what is > different compared with proc mixed. That is the way I do cross-check > and help me to understand. David's comments about high order arima and > complex time series model seems irrelevant, but always welcome.

Well, a lot of what I say is irrelevant. I often work on the 'million monkeys at a million typewriters' principle, and just filter the resultant. :-)

Seriously, I thought that eventually you might want to expand from an AR(1) model to something more complex, and I felt sure you wouldn't want to spend a ton of time fighting through the Yule-Walker equations.

But feel free to ignore whatever I say that's useless. Dale knows how to. :-)

HTH, David -- David Cassell, CSC Cassell.David@epa.gov Senior computing specialist mathematical statistician