From Stephen.Bond at cibc.com  Thu Jan 21 19:58:41 2010
From: Stephen.Bond at cibc.com (stephenb)
Date: Thu, 21 Jan 2010 10:58:41 -0800 (PST)
Subject: [Rd] arima with multiplicative season
Message-ID: <1264100321300-1050821.post@n4.nabble.com>


To: developers working on arima

is there a relatively easy way to achieve true multiplicative seasonal
effect and does multiplicative SMA make sense?

some books refer to the seasonal arima as multiplicative, because of the
multiplicative effect wrt to the ARMA spec:

(1-Bs)(1-aB)y = (1+bB)e

however the seasonal effect itself is still additive as we take the
difference between y(t) and y(t-s). 
I can achieve multiplicative differencing/division by creating a series
y(t)/y(t-s) and then fit regular ARIMA on that. In this case the SAR
coefficient is redundant I think as this simply scales the whole series. but
I am not sure if specifying a model with multiplicative SMA, where the
coefficient is estimated makes sense:

instead of e(t) - b*e(t-s) 

b*e(t)/e(t-s)

please, comment.
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[Rd] arima with multiplicative season
stephenb