Vector error-correction model (VECM) — morie

Native Johansen (1991) reduced-rank maximum-likelihood estimation: concentrate out the short-run dynamics, solve the generalized eigenvalue problem on the canonical-correlation matrices, and take the leading coint_rank eigenvectors as the cointegrating space. Replaces the urca::ca.jo + vars::vec2var delegation; the eigenvalues/vectors are cross-validated against urca in tests.

Usage

morie_vecm(Y, k_ar = 1, coint_rank = 1)

Arguments

Y: Numeric matrix (T x k) of I(1) candidate series.
k_ar: Number of lagged differences. Default 1.
coint_rank: Cointegration rank. Default 1.

Value

Named list with alpha, beta, Gamma, Sigma, eigenvalues, loglik, n, k, rank, method.

Examples

morie_vecm(Y = matrix(rnorm(100), 50, 2))
#> $alpha
#>          [,1]
#> y1 -0.5821343
#> y2 -0.7283620
#> 
#> $beta
#>         [,1]
#> y1 0.7332758
#> y2 1.1276966
#> 
#> $Gamma
#> $Gamma[[1]]
#>            y1          y2
#> y1 -0.7594522 -0.09695013
#> y2 -0.4439006 -0.88142538
#> 
#> 
#> $Sigma
#>            y1         y2
#> y1 1.07629603 0.08321452
#> y2 0.08321452 1.16027218
#> 
#> $eigenvalues
#> [1] 0.4397714 0.3424878
#> 
#> $loglik
#> [1] -137.2404
#> 
#> $n
#> [1] 50
#> 
#> $k
#> [1] 2
#> 
#> $rank
#> [1] 1
#> 
#> $method
#> [1] "VECM via native Johansen reduced-rank ML"
#>