# [R] Multivariate EWMA covariance estimator?

Neuman Co neumancohu at gmail.com
Sun Jun 2 19:03:29 CEST 2013

```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)){
>> 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
>
>

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