ind_Student_densities_Cpp: Calculate log independent multivariate Student's t densities

In sstvars: Toolkit for Reduced Form and Structural Smooth Transition Vector Autoregressive Models

Calculate log independent multivariate Student's t densities

Description

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.

Usage

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

Arguments

obs	a (T \times d) matrix such that the ith 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 ith 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 mth 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.

Details

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

Value

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

sstvars documentation built on April 11, 2025, 5:47 p.m.