loglik_normal function

Calculates the log-likelihood of a multivariate normal distribution.

loglik_normal(u, sigma)

Arguments

• u: a $K \times T$ matrix of residuals.
• sigma: a $K \times K$ or $KT \times K$ variance-covariance matrix.

Details

The log-likelihood is calculated for each vector in period $t$ as

, where $u_t = y_t - \mu_t$.

Examples

# 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)