gmvarkit (version 2.1.4)

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

Description

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

Usage

uncond_moments(gsmvar)

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.

Arguments

gsmvar

an object of class 'gsmvar', typically created with fitGSMVAR or GSMVAR.

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.

• Lütkepohl 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. 2025. A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics, 43, 1, 44-54.

• Virolainen S. 2022. Gaussian and Student's t mixture vector autoregressive model with application to the asymmetric effects of monetary policy shocks in the Euro area. Unpublished working paper, available as arXiv:2109.13648.

See Also

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

Examples

# GMVAR(1,2), d=2 model:
params12 <- c(0.55, 0.112, 0.344, 0.055, -0.009, 0.718, 0.319, 0.005,
 0.03, 0.619, 0.173, 0.255, 0.017, -0.136, 0.858, 1.185, -0.012,
 0.136, 0.674)
mod12 <- GSMVAR(gdpdef, p=1, M=2, params=params12)
uncond_moments(mod12)

# Structural GMVAR(2, 2), d=2 model identified with sign-constraints:
params22s <- c(0.36, 0.121, 0.484, 0.072, 0.223, 0.059, -0.151, 0.395,
 0.406, -0.005, 0.083, 0.299, 0.218, 0.02, -0.119, 0.722, 0.093, 0.032,
 0.044, 0.191, 0.057, 0.172, -0.46, 0.016, 3.518, 5.154, 0.58)
W_22 <- matrix(c(1, 1, -1, 1), nrow=2, byrow=FALSE)
mod22s <- GSMVAR(gdpdef, p=2, M=2, params=params22s, structural_pars=list(W=W_22))
mod22s
uncond_moments(mod22s)