[Rd] arima with multiplicative season

From: stephenb <Stephen.Bond_at_cibc.com>
Date: Thu, 21 Jan 2010 10:58:41 -0800 (PST)

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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