quantile_residuals: Calculate multivariate quantile residuals of a GMVAR, StMVAR,...

In saviviro/gmvarkit: Estimate Gaussian and Student's t Mixture Vector Autoregressive Models

Calculate multivariate quantile residuals of a GMVAR, StMVAR, or G-StMVAR model

Description

quantile_residuals calculates multivariate quantile residuals (proposed by Kalliovirta and Saikkonen 2010) for a GMVAR, StMVAR, or G-StMVAR model.

Usage

quantile_residuals(gsmvar)

Arguments

gsmvar

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

Value

Returns ((n_obs-p) x d) matrix containing the multivariate quantile residuals, j:th column corresponds to the time series in the j:th column of the data. The multivariate quantile residuals are calculated so that the first column quantile residuals are the "unconditioned ones" and the rest condition on all the previous ones in numerical order. Read the cited article by Kalliovirta and Saikkonen 2010 for details.

References

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

• Kalliovirta L. and Saikkonen P. 2010. Reliable Residuals for Multivariate Nonlinear Time Series Models. Unpublished Revision of HECER Discussion Paper No. 247.

• 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 Unpublished working paper, available as arXiv:2109.13648.

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

See Also

fitGSMVAR, GSMVAR, quantile_residual_tests, diagnostic_plot, predict.gsmvar, profile_logliks

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)
quantile_residuals(mod12)

# GMVAR(2,2), d=2 model with mean-parametrization:
params22 <- c(0.869, 0.549, 0.223, 0.059, -0.151, 0.395, 0.406, -0.005,
 0.083, 0.299, 0.215, 0.002, 0.03, 0.576, 1.168, 0.218, 0.02, -0.119,
 0.722, 0.093, 0.032, 0.044, 0.191, 1.101, -0.004, 0.105, 0.58)
mod22 <- GSMVAR(gdpdef, p=2, M=2, params=params22, parametrization="mean")
quantile_residuals(mod22)

# 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))
quantile_residuals(mod22s)

saviviro/gmvarkit documentation built on Jan. 4, 2025, 12:52 p.m.