[R] Multivariate EWMA covariance estimator?

[Berend Hasselman]

On 02-06-2013, at 19:03, Neuman Co <neumancohu at gmail.com> wrote:

> 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?
> 

I don't know but maybe something like this

1/sum(lambda^((1:100)-1))/(1-lambda)

which in your case is 1.000027

Berend

> 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