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 <[email protected]>: > > On 02-06-2013, at 15:17, Neuman Co <[email protected]> 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 ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
