Construct the companion matrix of an GARCH model

Construct the companion matrix of an GARCH model

GARCH_companion_matrix(alpha = 0, beta = 0)

Arguments

phi

numeric vector of length p, AR parameters.

theta

numeric vector of length q, MA parameters.

Value

numeric matrix of size p+q x p+q.

Note

Version 1.0.3

Examples

# ARCH(1) / GARCH(1) ~ Base 2 x 2
GARCH_companion_matrix(alpha = c(0.4))
#>      [,1] [,2]
#> [1,]    0  0.4
#> [2,]    0  0.0
#> attr(,"arOrder")
#> [1] 1
#> attr(,"maOrder")
#> [1] 1
GARCH_companion_matrix(beta = c(0.4))
#>      [,1] [,2]
#> [1,]  0.4    0
#> [2,]  0.0    0
#> attr(,"arOrder")
#> [1] 1
#> attr(,"maOrder")
#> [1] 1
# Only ARCH + 1 column of zero
GARCH_companion_matrix(alpha = c(0.4, 0.3, 0.1))
#>      [,1] [,2] [,3] [,4]
#> [1,]    0  0.4  0.3  0.1
#> [2,]    1  0.0  0.0  0.0
#> [3,]    0  1.0  0.0  0.0
#> [4,]    0  0.0  0.0  0.0
#> attr(,"arOrder")
#> [1] 1
#> attr(,"maOrder")
#> [1] 3
# Only GARCH + 1 column of zero
GARCH_companion_matrix(beta = c(0.4, 0.3, 0.1))
#>      [,1] [,2] [,3] [,4]
#> [1,]  0.4  0.3  0.1    0
#> [2,]  0.0  0.0  0.0    0
#> [3,]  0.0  1.0  0.0    0
#> [4,]  0.0  0.0  1.0    0
#> attr(,"arOrder")
#> [1] 3
#> attr(,"maOrder")
#> [1] 1
# FULL
GARCH_companion_matrix(c(0.4, 0.2), c(0.3, 0))
#>      [,1] [,2] [,3] [,4]
#> [1,]  0.3    0  0.4  0.2
#> [2,]  1.0    0  0.0  0.0
#> [3,]  0.0    0  0.0  0.0
#> [4,]  0.0    0  1.0  0.0
#> attr(,"arOrder")
#> [1] 2
#> attr(,"maOrder")
#> [1] 2