[R] Multivariate EWMA covariance estimator?

[Neuman Co]

Again, a big thanks for your answer.

On this webpage:
http://financetrainingcourse.com/education/2010/03/master-class-calculating-value-at-risk-var-final-steps/

I found, that I have to rescale by dividing the weights calculated in
Step B2 by 1-?n

The "?" is the lambda, since the webpage cannot display it, I also
found it on another webpage, therefore, I changed my code to the
following:

dummy2<-lambda^(a-1)/(1-lambda^100)*t(datamatrix[(i-a),]-t(meanvalues))%*%(datamatrix[(i-a),]-t(meanvalues))


Do you think this is correct?

One further question: You also told me, that I do not have to
initialize my dummy2, what does this mean? I wrote dummy2<-0 because I
have to create this variable before using it for the loop?

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



-- 
Neumann, Conrad