Calculates the log-likelihood of a multivariate normal distribution.
Calculates the log-likelihood of a multivariate normal distribution.
loglik_normal(u, sigma)
u |
a K \times T matrix of residuals. |
sigma |
a K \times K or KT \times K variance-covariance matrix. |
The log-likelihood is calculated for each vector in period t as
-\frac{K}{2} \ln 2π - \frac{1}{2} \ln |Σ_t| -\frac{1}{2} u_t^\prime Σ_t^{-1} u_t
, where u_t = y_t - μ_t.
# Load data
data("e1")
e1 <- diff(log(e1))
# Generate VAR model
data <- gen_var(e1, p = 2, deterministic = "const")
y <- t(data$data$Y)
x <- t(data$data$Z)
# LS estimate
ols <- tcrossprod(y, x) %*% solve(tcrossprod(x))
# Residuals
u <- y - ols %*% x # Residuals
# Covariance matrix
sigma <- tcrossprod(u) / ncol(u)
# Log-likelihood
loglik_normal(u = u, sigma = sigma)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.