# [R-SIG-Finance] Multivariate GARCH

Charles Evans cevans at chyden.net
Thu Dec 9 03:39:59 CET 2010

```Currently, I am working on an analysis of ETF premiums.  I have
estimated ECMs for my sample, but the error terms exhibit ARCH behavior.

Is there a more straightforward way to estimate a multivariate GARCH
model than mgarch or mgarchBEKK?  I have searched for a usable
tutorial, and I have been unable to find any other than Jeff Ryan's
post from 2007:

https://stat.ethz.ch/pipermail/r-sig-finance/2007q4/001833.html

and Ruey Tsay's transcript at:

http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2010/fGarch.txt

Can anyone direct me to a tutorial that lays out how one estimates a
multivariate GARCH model in R?  I'm not asking for a lesson in basic
econometrics, just an R-related URL that a researcher in a hurry can
use.

Specifically, I want to fit a model of the following form for a sample
of ETFs:

p = e + n + [GARCH factors] + v, where

p: price returns
e: lagged error terms from a first-pass regression of p on n
n: net asset value (NAV) returns
v: white noise error term

I have tried:

garchFit(p ~ garch(1,1), data=x.data, trace=F)

but I get exactly the same results as when I run:

garchFit(~ garch(1,1), data=x.data, trace=F)

where

x.data <- cbind(timeSeries(p),timeSeries(e),timeSeries(n))
colnames(x.data) <- c("p","e","n")

Apparently, I am doing something wrong.  Any hints would be greatly
appreciated.

Sample Data:

p <- c(0.005678744, 0.010188880, 0.004402934, -0.008585791,
0.002392346, 0.000000000, 0.013999517, 0.006107606, 0.012220111,
0.003809968, -0.008796353, -0.011222938, 0.003052004, 0.011073019,
-0.005346363, -0.008778660, 0.009826939, 0.000930882, -0.006300336,
0.005020149)

n <- c(0.002903111, 0.013199136, 0.002619049, -0.009796972,
0.006343149, -0.004543832, 0.015105848, 0.007058022, 0.008869238,
0.011436617, -0.010623656, -0.014617579, 0.004231815, 0.011082062,
-0.002788106, -0.010055036, 0.008891027, 0.002559034, -0.008985415,
0.007590391)

e <- c(2.144238e-03, -8.760417e-04, 9.058546e-04, 2.124476e-03,
-1.831144e-03, 2.716139e-03, 1.598335e-03, 6.425588e-04, 3.986696e-03,
-3.648639e-03, -1.813267e-03, 1.592476e-03, 4.094507e-04,
3.919921e-04, -2.164148e-03, -8.801350e-04, 4.902445e-05,
-1.581071e-03, 1.110833e-03, -1.465173e-03)

Yours,

Charles Evans

```