Gaussian_densities_Cpp function

Calculate log multivariate Gaussian densities

Calculates logs of multivariate Gaussian densities with varying mean and varying covariance matrix AND EXCLUDING the constant term of the density (the constant is calculated and added in R code). The varying conditional covariance matrix is calculated within the function from the regime covariance matrices and transition weights.

Gaussian_densities_Cpp(obs, means, covmats, alpha_mt)

Arguments

• obs: a $(T \times d)$ matrix such that the $i$th row contains the vector $y_{i}=(y_{1i},...,y_{di})$ $(dx1)$. That is, the initial values are excluded but the last observations is included.

• means: a $(T \times d)$ matrix such that the $i$th row contains the conditional mean of the process $\mu_{y,i}$.

• covmats: a $(d \times d \times M)$ array such that the slice [, , m]

  contains the conditional covariance matrix of regime m.

• alpha_mt: a $(T \times M)$ matrix such that [t, m] contains the time t transition weights of the $m$th regime.

Returns

a numeric vector containing the multivariate Gaussian densities, excluding the constant term.