# [R] Multivariate EWMA covariance estimator?

Neuman Co neumancohu at gmail.com
Sun Jun 2 15:17:57 CEST 2013

```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)){
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?

Thanks a lot for your help!
--