sstvars (version 1.1.0)

diagnostic_plot: Residual diagnostic plot for a STVAR model

Description

diagnostic_plot plots a multivariate residual diagnostic plot for either autocorrelation, conditional heteroskedasticity, or distribution, or simply draws the residual time series.

Usage

diagnostic_plot(
  stvar,
  type = c("all", "series", "ac", "ch", "dist"),
  resid_type = c("standardized", "raw"),
  maxlag = 12
)

Value

No return value, called for its side effect of plotting the diagnostic plot.

Arguments

stvar

object of class "stvar"

type

which type of diagnostic plot should be plotted?

• "all" all below sequentially.

• "series" the residual time series.

• "ac" the residual autocorrelation and cross-correlation functions.

• "ch" the squared residual autocorrelation and cross-correlation functions.

• "dist" the residual histogram with theoretical density (dashed line) and QQ-plots.

resid_type

should standardized or raw residuals be used?

maxlag

the maximum lag considered in types "ac" and "ch".

Details

Auto- and cross-correlations (types "ac" and "ch") are calculated with the function acf from the package stats and the plot method for class 'acf' objects is employed.

If cond_dist == "Student" or "ind_Student", the estimates of the degrees of freedom parameters is used in theoretical densities and quantiles. If cond_dist == "ind_skewed_t", the estimates of the degrees of freedom and skewness parameters are used in theoretical densities and quantiles, and the quantile function is computed numerically.

References

• Anderson H., Vahid F. 1998. Testing multiple equation systems for common nonlinear components. Journal of Econometrics, 84:1, 1-36.

• Hansen B.E. 1994. Autoregressive Conditional Density estimation. Journal of Econometrics, 35:3, 705-730.

• Kheifets I.L., Saikkonen P.J. 2020. Stationarity and ergodicity of Vector STAR models. International Economic Review, 35:3, 407-414.

• Lanne M., Virolainen S. 2024. A Gaussian smooth transition vector autoregressive model: An application to the macroeconomic effects of severe weather shocks. Unpublished working paper, available as arXiv:2403.14216.

• 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.

• Kilian L., Lütkepohl H. 20017. Structural Vector Autoregressive Analysis. 1st edition. Cambridge University Press, Cambridge.

• Tsay R. 1998. Testing and Modeling Multivariate Threshold Models. Journal of the American Statistical Association, 93:443, 1188-1202.

• Virolainen S. 2024. Identification by non-Gaussianity in structural threshold and smooth transition vector autoregressive models. Unpublished working paper, available as arXiv:2404.19707.

See Also

Portmanteau_test, profile_logliks, fitSTVAR, STVAR, LR_test, Wald_test, Rao_test

Examples

## Gaussian STVAR p=1, M=2 model, with weighted relative stationary densities
# of the regimes as the transition weight function:
theta_122relg <- c(0.734054, 0.225598, 0.705744, 0.187897, 0.259626, -0.000863,
  -0.3124, 0.505251, 0.298483, 0.030096, -0.176925, 0.838898, 0.310863, 0.007512,
  0.018244, 0.949533, -0.016941, 0.121403, 0.573269)
mod122 <- STVAR(data=gdpdef, p=1, M=2, params=theta_122relg)

# Autocorelation function of raw residuals for checking remaining autocorrelation:
diagnostic_plot(mod122, type="ac", resid_type="raw")

# Autocorelation function of squared standardized residuals for checking remaining
# conditional heteroskedasticity:
diagnostic_plot(mod122, type="ch", resid_type="standardized")

# Below, ACF of squared raw residuals, which is not very informative for evaluating
# adequacy to capture conditional heteroskedasticity, since it doesn't take into account
# the time-varying conditional covariance matrix of the model:
diagnostic_plot(mod122, type="ch", resid_type="raw")

# Similarly, below the time series of raw residuals first, and then the
# time series of standardized residuals. The latter is more informative
# for evaluating adequacy:
diagnostic_plot(mod122, type="series", resid_type="raw")
diagnostic_plot(mod122, type="series", resid_type="standardized")

# Also similarly, histogram and Q-Q plots are more informative for standardized
# residuals when evaluating model adequacy:
diagnostic_plot(mod122, type="dist", resid_type="raw") # Bad fit for GDPDEF
diagnostic_plot(mod122, type="dist", resid_type="standardized") # Good fit for GDPDEF

## Linear Gaussian VAR p=1 model:
theta_112 <- c(0.649526, 0.066507, 0.288526, 0.021767, -0.144024, 0.897103,
  0.601786, -0.002945, 0.067224)
mod112 <- STVAR(data=gdpdef, p=1, M=1, params=theta_112)
diagnostic_plot(mod112, resid_type="standardized") # All plots for std. resids
diagnostic_plot(mod112, resid_type="raw") # All plots for raw residuals