Multivariate EWMA covariance estimator?

Thanks a lot for your answer, one more question:
I now use 100 values, so not infinity values. That means I cut some
values off, so the weights will not sum up to one. With which factor
do I have to multiply the (1-lambda)*summe2 to rescale it? So that I
do not always underestimate the variance anymore?

2013/6/2 Berend Hasselman <bhh at xs4all.nl>:

On 02-06-2013, at 15:17, Neuman Co <neumancohu at gmail.com> wrote:

Hi,
since I want to calculate the VaR of a portfolio consiting of 4 assets
(returns saved into "eonreturn","henkelreturn" and so on) I have to
estimate the covariance matrix. I do not want to take the rectangular
version with equal weights, but the exponentially weighted moving
average in a multivariate version. I want to estimate a covariance
matrix at every time point t. Then I want to comput the VaR at this
time point t. Afterwards, I will look at the exceedances and do a
backtest.

I tried to implement it as follows (data attached):

lambda<-0.9

summe2<-0
dummy2<-0
covestiexpo<-list(NA)
meanvalues<-NA
for(i in 101:length(eonreturn)){
meanvalues<-matrix(c(mean(eonreturn[(i-100):(i-1)]),mean(henkelreturn[(i-100):(i-1)]),mean(siemensreturn[(i-100):(i-1)]),mean(adidasreturn[(i-100):(i-1)])),4)
for(a in 1:100){
dummy2<-lambda^(a-1)*t(datamatrix[(i-a),]-t(meanvalues))%*%(datamatrix[(i-a),]-t(meanvalues))
summe2<-summe2+dummy2
}
covestiexpo[[i]]<-(1-lambda)*summe2
}


So the covestieexpo[[101]] would be the covariance estimate for the
101th day, taking into account the last 100 observations. Now, the
problem is, that there seems to be something wrong, since the
covariance estimates are cleraly wrong, they seem to be too big. At
the beginning, compared to the normal covariance estimate the
difference is as follows:

covestiexpo[[101]]
          [,1]        [,2]        [,3]        [,4]
[1,] 0.004559042 0.002346775 0.004379735 0.003068916
[2,] 0.002346775 0.001978469 0.002536891 0.001909276
[3,] 0.004379735 0.002536891 0.005531590 0.003259803
[4,] 0.003068916 0.001909276 0.003259803 0.003140198



compared to cov(datamatrix[1:100,])
           [,1]         [,2]         [,3]        [,4]
[1,] 0.0018118239 0.0007432779 0.0015301070 0.001119120
[2,] 0.0007432779 0.0008355960 0.0009281029 0.000754449
[3,] 0.0015301070 0.0009281029 0.0021073171 0.001269626
[4,] 0.0011191199 0.0007544490 0.0012696257 0.001325716

So already here, it is obvious, that something is not correct, if I
look at a period far ahead:

covestiexpo[[1200]]

        [,1]      [,2]      [,3]      [,4]
[1,] 0.5312575 0.1939061 0.3419379 0.2475233
[2,] 0.1939061 0.3204951 0.2303478 0.2022423
[3,] 0.3419379 0.2303478 0.5288435 0.2943051
[4,] 0.2475233 0.2022423 0.2943051 0.4599648


you can see, that the values are way too large, so where is my mistake?

Without actual data this is an unverifiable statement.
But you probably have to move the statement

summe2 <- 0

to inside the i-forloop just before the a-forloop.

summe2 <- 0
for(a in 1:100){
?

so that summe2 is initialized to 0 every time you use it as an accumulator in the a-forloop.
Furthermore there is no need to initialize dummy2. It gets overwritten continuously.

Berend

-- 
Neumann, Conrad