[R-SIG-Finance] a problem with external regressors in rugarch

[alexios ghalanos]

Alec,

The ugarchfit method calls R's arima in order to quickly calculate a set
of starting values prior to the joint ARMA-GARCH estimation. From
arima's documentation:

"If am xreg term is included, a linear regression (with a constant term
if include.mean is true and there is no differencing) is fitted with an
ARMA model for the error term"

You've included:

1. An intercept (matrix of 1's)...this is how 'include.mean' in arima
routine is interpreted.
2. All the days of the week (X)

This results in perfect multicollinearity, which means that it is not
possible to invert the matrix and solve the problem (which is why
leaving one out works). This is typically known as the "dummy variable
trap".

Therefore:
1. Leave one (day) out
2. Pass a demeaned dataset and set include.mean=FALSE


-Alexios


On 04/10/2013 03:01, Alec Schmidt wrote:
> Hi everyone,
> 
> I'm struggling with adding external regressors X to arma+garch model using
> the following script:
> 
> spec1121ex = ugarchspec(variance.model = list(model = "sGARCH", garchOrder
> = c(2,1)),
>                   mean.model = list(armaOrder = c(1,1), include.mean =
> TRUE, external.regressors = X),
>                   distribution.model = "std")
> 
> fit1121ex<-ugarchfit(data=rt[,1], spec=spec1121ex)
> 
> The regressor matrix X (currently) has the following form:
> 
> head(X)     [,1] [,2] [,3] [,4] [,5]
> [1,]    0    0    0    0    1
> [2,]    1    0    0    0    0
> [3,]    0    1    0    0    0
> [4,]    0    0    1    0    0
> [5,]    0    0    0    1    0
> [6,]    0    0    0    0    1
> 
> 
> When I run ugarchfit, I get an error:
> 
> Error in optim(init[mask], armaCSS, method = optim.method, hessian = TRUE,  :
>   non-finite value supplied by optim
> 
> I make X from the table rtn
> 
>> head(rtn)                    SPY Mon Tue Wed Thu Fri
> 2009-01-05 -0.001189061   1   0   0   0   0
> 2009-01-06  0.006640603   0   1   0   0   0
> 2009-01-07 -0.030479920   0   0   1   0   0
> 2009-01-08  0.004134247   0   0   0   1   0
> 2009-01-09 -0.021711980   0   0   0   0   1
> 2009-01-12 -0.024224590   1   0   0   0   0
> 
>> X<-matrix(cbind(rtn[,2], rtn[,3], rtn[,4], rtn[,5], rtn[,6]), ncol=5)
> 
> Surprisingly sript runs fine if I choose ncol<5, e.g.
>> X<-matrix(cbind(rtn[,3], rtn[,4], rtn[,5], rtn[,6]), ncol=4)
> 
> or
> 
>> X<-matrix(cbind(rtn[,2], rtn[,3], rtn[,4], rtn[,5]), ncol=4)
> 
> Thanks a lot,
>