gmvarkit (version 1.4.1)

uncond_moments: Calculate the unconditional mean, variance, the first p autocovariances, and the first p autocorrelations of a GMVAR process

Description

uncond_moments calculates the unconditional mean, variance, the first p autocovariances, and the first p autocorrelations of the given GMVAR process.

Usage

uncond_moments(gmvar)

Arguments

gmvar

an object of class 'gmvar' created with fitGMVAR or GMVAR.

Value

Returns a list with three components:

$uncond_mean

a length d vector containing the unconditional mean of the process.

$autocovs

an \((d x d x p+1)\) array containing the lag 0,1,...,p autocovariances of the process. The subset [, , j] contains the lag j-1 autocovariance matrix (lag zero for the variance).

$autocors

the autocovariance matrices scaled to autocorrelation matrices.

Details

The unconditional moments are based on the stationary distribution of the process.

References

• Kalliovirta L., Meitz M. and Saikkonen P. 2016. Gaussian mixture vector autoregression. Journal of Econometrics, 192, 485-498.

• L<U+00FC>tkepohl H. 2005. New Introduction to Multiple Time Series Analysis, Springer.

• McElroy T. 2017. Computation of vector ARMA autocovariances. Statistics and Probability Letters, 124, 92-96.

• Virolainen S. 2020. Structural Gaussian mixture vector autoregressive model. Unpublished working paper, available as arXiv:2007.04713.

See Also

Other moment functions: cond_moments(), get_regime_autocovs(), get_regime_means()

Examples

# NOT RUN {
# GMVAR(1,2), d=2 model:
params122 <- c(0.623, -0.129, 0.959, 0.089, -0.006, 1.006, 1.746,
 0.804, 5.804, 3.245, 7.913, 0.952, -0.037, -0.019, 0.943, 6.926,
 3.982, 12.135, 0.789)
mod122 <- GMVAR(p=1, M=2, d=2, params=params122)
uncond_moments(mod122)

# GMVAR(2,2), d=2 model with AR-parameters restricted to be
# the same for both regimes:
C_mat <- rbind(diag(2*2^2), diag(2*2^2))
params222c <- c(1.031, 2.356, 1.786, 3.000, 1.250, 0.060, 0.036,
 1.335, -0.290, -0.083, -0.047, -0.356, 0.934, -0.152, 5.201, 5.883,
 3.560, 9.799, 0.368)
mod222c <- GMVAR(p=2, M=2, d=2, params=params222c, constraints=C_mat)
uncond_moments(mod222c)

# Structural GMVAR(2, 2), d=2 model identified with sign-constraints:
params222s <- c(1.03, 2.36, 1.79, 3, 1.25, 0.06, 0.04, 1.34, -0.29,
 -0.08, -0.05, -0.36, 1.2, 0.05, 0.05, 1.3, -0.3, -0.1, -0.05, -0.4,
  0.89, 0.72, -0.37, 2.16, 7.16, 1.3, 0.37)
W_222 <- matrix(c(1, 1, -1, 1), nrow=2, byrow=FALSE)
mod222s <- GMVAR(p=2, M=2, d=2, params=params222s, structural_pars=list(W=W_222))
uncond_moments(mod222s)
# }