Of course, ARIMA models are easily fitted in R. I estimate a model, in which the i-th error term of the ARIMA model shall depend on the three errors before (seasonal volatility). Is there any way to model seasonal volatility in R without using KFAS and/or similar packages? Does there exist any plug-in-method in any R-package, which is ready to use?
If it was a calendar seasonal (month of year, day of week, etc.) you could easily include a dummy variable using the model of Jones, Lamont and Lumsdaine (Journal of Financial Economics, 1998). I use the method in my paper on Treasury Auctions.
Looks like you are looking for more of a time series seasonal. My intuition says to start with an ARIMA-GARCH(1,1) and just adapt the variance equation to meet your specification above.
There are some very good GARCH packages out there. I haven't done any of this in R but there are probably some out there. EViews has "likelihood object" that can be used to create customized GARCH models. Kevin Sheppard has a free Matlab Garch package.
Oxmetrics has an outstanding GARCH package created by Sebastian Laurent. I think there is a "console" version that is free for academics.
Looks like the free Ox version and G@rch package is available for version 6. Download link is at the end of chapter 1 http://www.timberlake.co.uk/slaurent/G@RCH/default.htm
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