atRisk (version 0.2.0)

f_distrib: Distribution

Description

This function is used to estimate the parameters of the distribution for each period (mean and standard deviation for Gaussian Distribution, xi, omega and alpha for Skew-Normal Distribution, and xi, omega, alpha, and nu for t-student Distribution) based on the quantile regression results (Koenker and Basset, 1978). See Adrian et al. (2019) and Adrian et al. (2022) for more details on the estimation steps.

Usage

f_distrib(type_function, compile_qt, starting_values, tolerance = 1e-06)

Value

Dataframe with the parameters of the distribution for each period. This dataframe includes out of sample values of the paramateres if newdata has been specified in f_compile_quantile.

Arguments

type_function

String argument : "gaussian" for Normal Distribution, "skew-gaussian" for Skew-Normal Distribution or "skew-t" for t-student Distribution

compile_qt

List containing the results of f_compile_quantile function

starting_values

Numeric vector with initial values for optimization

tolerance

Numeric optional for the convergence tolerance. Iteration is terminated when the absolute difference in function value between successive iteration is below tol (default value = 1.e-06).

References

Adrian, Tobias, Nina Boyarchenko, and Domenico Giannone. "Vulnerable growth." American Economic Review 109.4 (2019): 1263-89.

Adrian, Tobias, et al. "The term structure of growth-at-risk." American Economic Journal: Macroeconomics 14.3 (2022): 283-323.

Koenker, Roger, and Gilbert Bassett Jr. "Regression quantiles." Econometrica: journal of the Econometric Society (1978): 33-50.

Azzalini, Adelchi. "The skew-normal and related families." Vol. 3. Cambridge University Press (2013).

Examples

# \donttest{
# Import data
data("data_euro")

# Data process
PIB_euro_forward_4 = data_euro["GDP"][c(5:length(data_euro["GDP"][,1])),]
FCI_euro_lag_4 = data_euro["FCI"][c(1:(length(data_euro["GDP"][,1]) - 4)),]
CISS_euro_lag_4 = data_euro["CISS"][c(1:(length(data_euro["GDP"][,1]) - 4)),]

# for a gaussian
quantile_target <- as.vector(c(0.25,0.75))
results_quantile_reg <- f_compile_quantile(qt_trgt=quantile_target,
v_dep=PIB_euro_forward_4,
v_expl=cbind(FCI_euro_lag_4, CISS_euro_lag_4))

results_g <- f_distrib(type_function="gaussian",
compile_qt=results_quantile_reg,
starting_values=c(0, 1))

# for a skew-t
quantile_target <- as.vector(c(0.10,0.25,0.75,0.90))
results_quantile_reg <- f_compile_quantile(qt_trgt=quantile_target,
v_dep=PIB_euro_forward_4,
v_expl=cbind(FCI_euro_lag_4, CISS_euro_lag_4))

results <- f_distrib(type_function="skew-t",
compile_qt=results_quantile_reg,
starting_values=c(0, 0.5, 0, 2), tolerance=1e-05)
# }