f_distrib_histo {matrisk}

Historical distributions

Description

This function is based on f_distrib function (Adrian et al., 2019; Adrian et al., 2022) and is used to get historical estimation of empirical distributions and associated parameters. Results allow to realize a 3D graphical representation.

Usage

f_distrib_histo(
  qt_trgt,
  v_dep,
  v_expl,
  type_function,
  starting_values,
  step,
  x_min,
  x_max
)

Arguments

qt_trgt

Numeric vector, dim k, of k quantiles for different qt-estimations

v_dep

Numeric vector of the dependent variable

v_expl

Numeric vector of the (k) explanatory variable(s)

type_function

String argument : "gaussian" for normal distribution or "skew-t" for t-student distribution

starting_values

Numeric vector with initial values for optimization

step

Numeric argument for accuracy graphics abscissa

x_min

Numeric optional argument (default value = -15)

x_max

Numeric optional argument (default value = 10)

Value

A list with:

distrib_histo

Numeric matrix with historical values of x, y and t

param_histo

Numeric matrix containing the parameters of the distribution for each period

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.

Examples

# 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)),]

results_histo <- f_distrib_histo(qt_trgt=c(0.10,0.25,0.75,0.90), v_dep=PIB_euro_forward_4,
v_expl=cbind(FCI_euro_lag_4,CISS_euro_lag_4),
type_function="skew-t",
starting_values=c(0, 1, -0.5, 1.3),
step=5, x_min=-10, x_max=5)

library(plot3D) # load
scatter3D(results_histo$distrib_histo[,3],
results_histo$distrib_histo[,1],
results_histo$distrib_histo[,2],
pch = 10,  theta = 70, phi = 10,
main = "Distribution of GDP Growth over time - Euro Area",
xlab = "Date",
ylab ="Pib",
zlab="", cex = 0.3)