Quickly estimate a VAR(p) model using Armadillo's inverse function.
.VAR(x, p = 1L)data numeric matrix with time series in columns - without missing values.
positive integer. The lag order of the VAR.
A list containing matrices Y = x[-(1:p), ], X which contains lags 1 - p of x combined column-wise,
A which is the \(np \times n\) transition matrix, where n is the number of series in x, and the VAR residual matrix res = Y - X %*% A.
A list with the following elements:
Yx[-(1:p), ].
Xlags 1 - p of x combined column-wise.
A\(np \times n\) transition matrix, where n is the number of series in x.
resVAR residual matrix: Y - X %*% A.
var = .VAR(diff(EuStockMarkets), 3)
str(var)
#> List of 4
#> $ Y : num [1:1856, 1:4] -2.88 -7.55 20.14 9.42 -4.7 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
#> $ X : num [1:1856, 1:12] 14.53 -2.88 -7.55 20.14 9.42 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:12] "DAX" "SMI" "CAC" "FTSE" ...
#> $ A : num [1:12, 1:4] 0.00946 -0.09901 0.04544 0.09475 0.02456 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : chr [1:12] "DAX" "SMI" "CAC" "FTSE" ...
#> .. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
#> $ res: num [1:1856, 1:4] -3.39 -5.54 21.51 5.04 -4.91 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
var$A
#> DAX SMI CAC FTSE
#> DAX 0.009458998 0.027283428 -0.01093944 0.025490277
#> SMI -0.099010841 -0.034164357 -0.06651577 -0.094882142
#> CAC 0.045444935 0.037822109 0.03972168 -0.018984419
#> FTSE 0.094745867 0.143551499 0.09179713 0.196154434
#> DAX 0.024559851 0.001705899 0.01593365 0.023913757
#> SMI -0.021282229 0.018452931 -0.02701831 -0.029297417
#> CAC 0.063422809 0.109479561 0.08450745 0.026931128
#> FTSE -0.076819232 -0.097909530 -0.06820239 -0.022626747
#> DAX -0.053821302 -0.124261943 -0.01894164 -0.040102476
#> SMI 0.001254346 -0.018010725 0.01927024 -0.001231464
#> CAC 0.049037401 0.100660797 -0.06168014 0.066430851
#> FTSE 0.037908210 0.122676727 0.01831834 -0.004359654
rm(var)