Pearson_residuals: Calculate multivariate Pearson residuals of a GMVAR, StMVAR,...

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

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

Description

Pearson_residuals calculates multivariate Pearson residuals for a GMVAR, StMVAR, or G-StMVAR model.

Usage

Pearson_residuals(gsmvar, standardize = TRUE)

Arguments

gsmvar	an object of class 'gsmvar', typically created with fitGSMVAR or GSMVAR.
standardize	Should the residuals be standardized? Use FALSE to obtain raw residuals.

Value

Returns ((n_obs-p) x d) matrix containing the residuals, j:th column corresponds to the time series in the j:th column of the data.

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 Unpublished Revision of HECER Discussion Paper No. 247.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. (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 Unpublished working paper, available as arXiv:2109.13648.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

fitGSMVAR, GSMVAR, quantile_residuals, diagnostic_plot

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)
Pearson_residuals(mod12, standardize=FALSE) # Raw residuals
Pearson_residuals(mod12, standardize=TRUE) # Standardized to identity cov.matrix.

# 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))
Pearson_residuals(mod22s, standardize=FALSE) # Raw residuals
Pearson_residuals(mod22s, standardize=TRUE) # Standardized to identity cov.matrix.

saviviro/gmvarkit documentation built on March 8, 2024, 4:15 a.m.