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Some examples from here of the rugarch R package, used in a Sage Worksheet on SageMathCloud.

%auto
%default_mode r

library(rugarch)

data(sp500ret)
# create a cluster object to be used as part of this demonstration
cluster = makePSOCKcluster(5)

spec = ugarchspec()
show(spec)
*---------------------------------* * GARCH Model Spec * *---------------------------------* Conditional Variance Dynamics ------------------------------------ GARCH Model : sGARCH(1,1) Variance Targeting : FALSE Conditional Mean Dynamics ------------------------------------ Mean Model : ARFIMA(1,0,1) Include Mean : TRUE GARCH-in-Mean : FALSE Conditional Distribution ------------------------------------ Distribution : norm Includes Skew : FALSE Includes Shape : FALSE Includes Lambda : FALSE 
nrow(expand.grid(GARCH = 1:14, VEX = 0:1, VT = 0:1, Mean = 0:1, ARCHM = 0:2, ARFIMA = 0:1, MEX = 0:1, DISTR = 1:10))
[1] 13440