Score function of parametric S-vine models
Arguments
- x
the data.
- model
S-vine model (inheriting from svine_dist).
- cores
number of cores to use.
Value
An n-by-k matrix, where n = NROW(x) - model$copula$p and k
is the total number of model parameters. The rows correspond to the
effective time points after the first p observations. Parameters are
ordered as follows:
marginal parameters, copula parameters of first tree, copula parameters of
second tree, etc. Duplicated parameters in the copula model are omitted.
Examples
data(returns)
dat <- returns[1:100, 1:2]
# fit parametric S-vine model with Markov order 1
model <- svine(dat, p = 1, family_set = "parametric")
# Implementation of asymptotic variances
I <- cov(svine_scores(dat, model))
H <- svine_hessian(dat, model)
Hi <- solve(H)
n_eff <- nrow(dat) - model$copula$p
Hi %*% I %*% t(Hi) / n_eff
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.663430e-06 -7.345803e-08 1.263944e-06 -1.929607e-07 -1.180159e-05
#> [2,] -7.345803e-08 2.770406e-07 -9.746336e-08 1.595365e-07 1.513774e-06
#> [3,] 1.263944e-06 -9.746336e-08 2.336204e-06 -2.406471e-07 2.508189e-05
#> [4,] -1.929607e-07 1.595365e-07 -2.406471e-07 3.838785e-07 -7.006600e-06
#> [5,] -1.180159e-05 1.513774e-06 2.508189e-05 -7.006600e-06 2.930565e-03
#> [6,] 7.395518e-05 1.476121e-04 2.485149e-04 1.081140e-04 2.803207e-02
#> [7,] 2.223716e-05 3.223684e-08 2.475948e-06 -4.471570e-08 5.204545e-04
#> [8,] -5.252907e-04 2.693214e-04 -5.935837e-04 -4.655805e-06 -1.578135e-02
#> [9,] 2.030250e-05 6.309618e-07 1.169314e-05 1.269796e-05 -1.280164e-03
#> [,6] [,7] [,8] [,9]
#> [1,] 7.395518e-05 2.223716e-05 -5.252907e-04 2.030250e-05
#> [2,] 1.476121e-04 3.223684e-08 2.693214e-04 6.309618e-07
#> [3,] 2.485149e-04 2.475948e-06 -5.935837e-04 1.169314e-05
#> [4,] 1.081140e-04 -4.471570e-08 -4.655805e-06 1.269796e-05
#> [5,] 2.803207e-02 5.204545e-04 -1.578135e-02 -1.280164e-03
#> [6,] 2.523648e+00 2.532996e-02 -5.715128e-02 2.020138e-02
#> [7,] 2.532996e-02 1.294684e-02 -1.089806e-01 8.937680e-04
#> [8,] -5.715128e-02 -1.089806e-01 6.862175e+00 -1.027885e-02
#> [9,] 2.020138e-02 8.937680e-04 -1.027885e-02 9.113254e-03