gmvarkit (version 1.4.1)

quantile_residuals: Calculate multivariate quantile residuals of a GMVAR model

Description

quantile_residuals calculates multivariate quantile residuals (described by Kalliovirta and Saikkonen 2010) for a GMVAR model.

Usage

quantile_residuals(gmvar)

Arguments

gmvar

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

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 Unpublished Revision of HECER Discussion Paper No. 247.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. 2020. Structural Gaussian mixture vector autoregressive model. Unpublished working paper, available as arXiv:2007.04713.

See Also

fitGMVAR, GMVAR, quantile_residual_tests, diagnostic_plot, predict.gmvar, profile_logliks

Examples

# NOT RUN {
# These examples use the data 'eurusd' which comes with the
# package, but in a scaled form.
data <- cbind(10*eurusd[,1], 100*eurusd[,2])
colnames(data) <- colnames(eurusd)

# 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(data, p=1, M=2, params=params122)
quantile_residuals(mod122)

# GMVAR(2,2), d=2 model with mean-parametrization:
params222 <- c(-11.904, 154.684, 1.314, 0.145, 0.094, 1.292, -0.389,
 -0.070, -0.109, -0.281, 0.920, -0.025, 4.839, 11.633, 124.983, 1.248,
  0.077, -0.040, 1.266, -0.272, -0.074, 0.034, -0.313, 5.855, 3.570,
  9.838, 0.740)
mod222 <- GMVAR(data, p=2, M=2, params=params222, parametrization="mean")
quantile_residuals(mod222)

# 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(data, p=2, M=2, params=params222s, structural_pars=list(W=W_222))
quantile_residuals(mod222s)

# 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(data, p=2, M=2, params=params222c, constraints=C_mat)
quantile_residuals(mod222c)

# GMVAR(2,2), d=2 model with AR-parameters restricted to be
# the same for both regimes and the non-diagonal elements of
# the coefficient matrices constrained to zero.
tmp <- matrix(c(1, rep(0, 10), 1, rep(0, 8), 1, rep(0, 10), 1),
 nrow=2*2^2, byrow=FALSE)
C_mat2 <- rbind(tmp, tmp)
params222c2 <- c(0.355, 3.193, -0.114, 2.829, 1.263, 1.338, -0.292,
 -0.362, 5.597, 3.456, 9.622, 0.982, -0.327, 5.236, 0.650)
mod222c2 <- GMVAR(data, p=2, M=2, params=params222c2,
  constraints=C_mat2)
quantile_residuals(mod222c)
# }