I have a large XTS object which is the result of a correlation calculation using a sliding window across an XTS ZOO object of 12 x 12 variables for 1343 data points in time.
My large XTS object is structured as follows, rows represent time and columns represent the correlation combinations. A simplified example is shown below:
AA BA CA AB BB CB AC BC CC
t1 1 .1 -.4 .1 1 .3 -.4 .3 1
t2 1 .4 .8 .4 1 .2 .8 .2 1
t3 1 .5 .5 .5 1 .3 .5 .3 1
t4 1 .6 .1 .6 1 .7 .1 .7 .1
Correct me if I'm wrong but I believe the eigen() function in R requires a square matrix to calculate the eigenvalues of the matrix lambda 1,2 and 3?
How can I square the xts object above to find the eigenvalues and vectors with each matrix across time?
I'm guessing I'll have a matrix for each time period (1-4) in the XTS object above and the matrix should be constructed by taking the first 3 values (1 .1 -.4) and putting them into the first column, again the next three values (.1 1 .3) and this goes into the second column and finally the last three values of row one (-.4 .3 1) go into the last column to make up the 3 x 3 matrix which is shown below:
matrix for t1
A B C
A 1 .1 -.4
B .1 1 .3
C -.4 .3 1
Maybe the transformation from the XTS object is not required to calculate the eigenvalues but if I step through it in my head these are the steps required to calculate the eigenvalues for my XTS object.
Ideally the eigenvalues from each matrix would then be stored in a dataframe or matrix, in the case above I would have a dataframe of 12 observations of 3 variables or a matrix of 3 x 4.
Can anyone tell me if I'm going about this the wrong way and whether eigen() can take the XTS object in it's current form and calculate the eigenvalues?
For demonstration purposes, I'm only returning the greatest of the eigenvalues set, but you can modify the code to return anything you need.
library(xts)
dfx <- structure(c(1, 1, 1, 1, 0.1, 0.4, 0.5, 0.6, -0.4, 0.8, 0.5, 0.1,
0.1, 0.4, 0.5, 0.6, 1, 1, 1, 1, 0.3, 0.2, 0.3, 0.7, -0.4, 0.8,
0.5, 0.1, 0.3, 0.2, 0.3, 0.7, 1, 1, 1, 1), .Dim = c(4L, 9L), .Dimnames = list(
NULL, c("AA", "BA", "CA", "AB", "BB", "CB", "AC", "BC", "CC"
)), index = structure(c(1167685200, 1167771600, 1167858000,
1167944400), tzone = "", tclass = c("POSIXct", "POSIXt")), .indexCLASS = c("POSIXct",
"POSIXt"), tclass = c("POSIXct", "POSIXt"), .indexTZ = "", tzone = "", class = c("xts",
"zoo"))
apply.daily(dfx, function(x) eigen(matrix(x, nrow = sqrt(length(x))))$values[1])
# [,1]
#2007-01-02 1.455287
#2007-01-03 1.984869
#2007-01-04 1.872842
#2007-01-05 1.972804