Student_densities_Cpp function

Calculate log multivariate Student's t densities

Calculates logs of multivariate Student t 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.

Student_densities_Cpp(obs, means, covmats, alpha_mt, df)

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.

• df: the degrees of freedom parameter value (assumed larger than two).

Returns

a numeric vector containing the multivariate Student's t densities, excluding the constant term.

Details

Note that the parametrization is with the covariance matrix and not the scale matrix.