uncond_moments {gmvarkit}

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)

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.

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.

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. (forthcoming). A statistically identified structural vector autoregression with endogenously switching volatility regime. Journal of Business & Economic Statistics.

• 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 Unpublished working paper, available as arXiv:2109.13648.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)