ind_Student_densities_Cpp function

Calculate log independent multivariate Student's t densities

Calculates logs of independent multivariate Student t densities with varying mean and impact matrix AND EXCLUDING the constant term of the density (the constant is calculated and added in R code). The varying impact matrix is calculated within the function from the impact matrices of the regimes and transition weights.

ind_Student_densities_Cpp(
  obs,
  means,
  impact_matrices,
  alpha_mt,
  distpars,
  minval,
  posdef_tol
)

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 $\mu_{y,i}$.
• impact_matrices: a size $d\times d \times M$ arma::cube (3D array in R), where each slice contains an invertible (d x d) impact matrix of each regime.
• alpha_mt: a $(T \times M)$ matrix such that [t, m] contains the time t transition weights of the $m$th regime.
• distpars: a numeric vector of length $d$, containing the degrees of freedom parameters for each component.
• minval: the value that will be returned if the parameter vector does not lie in the parameter space (excluding the identification condition).
• posdef_tol: numerical tolerance for positive definiteness of the error term covariance matrices: if the error term covariance matrix of any regime has eigenvalues smaller than this, the parameter is considered to be outside the parameter space. Note that if the tolerance is too small, numerical evaluation of the log-likelihood might fail and cause error.

Returns

A numeric vector of length $T$, where each element represents the computed density component for the corresponding observation.

Details

Returns minval if the impact matrix $B_t$ is not invertible for some t up to the numerical tolerance posdef_tol.