uncond_moments function

Calculate the unconditional means, variances, the first p autocovariances, and the first p autocorrelations of the regimes of the model.

uncond_moments calculates the unconditional means, variances, the first p autocovariances, and the first p autocorrelations of the regimes of the model.

uncond_moments(stvar)

Arguments

• stvar: object of class "stvar"

Returns

Returns a list with three components:

• $regime_means: a $M \times d$ matrix vector containing the unconditional mean of the regime $m$ in the $m$th column.
• $regime_vars: a $M \times d$ matrix vector containing the unconditional marginal variances of the regime $m$ in the $m$th column.
• $regime_autocovs: an $(d x d x p+1, M)$ array containing the lag 0,1,...,p autocovariances of the process. The subset [, , j, m] contains the lag j-1 autocovariance matrix (lag zero for the variance) for the regime $m$.
• $regime_autocors: the autocovariance matrices scaled to autocorrelation matrices.

Examples

# Two-variate Gaussian STVAR p=1, M=2 model with the weighted relative stationary
# densities of the regimes as the transition weight function:
theta_122relg <- c(0.734054, 0.225598, 0.705744, 0.187897, 0.259626, -0.000863,
-0.3124, 0.505251, 0.298483, 0.030096, -0.176925, 0.838898, 0.310863, 0.007512,
0.018244, 0.949533, -0.016941, 0.121403, 0.573269)
mod122 <- STVAR(data=gdpdef, p=1, M=2, params=theta_122relg, weight_function="relative_dens")

# Calculate the unconditional moments of model:
tmp122 <- uncond_moments(mod122)

# Print the various unconditional moments calculated:
tmp122$regime_means[,1] # Unconditional means of the first regime
tmp122$regime_means[,2] # Unconditional means of the second regime
tmp122$regime_vars[,1] # Unconditional variances of the first regime
tmp122$regime_vars[,2] # Unconditional variances of the second regime
tmp122$regime_autocovs[, , , 1] # a.cov. matrices of the first regime
tmp122$regime_autocovs[, , , 2] # a.cov. matrices of the second regime
tmp122$regime_autocors[, , , 1] # a.cor. matrices of the first regime
tmp122$regime_autocors[, , , 2] # a.cor. matrices of the second regime

# A two-variate linear Gaussian VAR p=1 model:
theta_112 <- c(0.649526, 0.066507, 0.288526, 0.021767, -0.144024, 0.897103,
 0.601786, -0.002945, 0.067224)
mod112 <- STVAR(data=gdpdef, p=1, M=1, params=theta_112)

# Calculate the unconditional moments of model:
tmp112 <- uncond_moments(mod112)

# Print the various unconditional moments calculated:
tmp112$regime_means # Unconditional means
tmp112$regime_vars # Unconditional variances
tmp112$regime_autocovs # Unconditional autocovariance matrices
tmp112$regime_autocovs[, , 1, 1] # a.cov. matrix of lag zero (of the first regime)
tmp112$regime_autocovs[, , 2, 1] # a.cov. matrix of lag one (of the first regime)
tmp112$regime_autocors # Unconditional autocorrelation matrices

References

• Lütkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.