Title: Macroeconomic-at-Risk
Version: 0.1.0
Description: The Macroeconomics-at-Risk (MaR) approach is based on a two-step semi-parametric estimation procedure that allows to forecast the full conditional distribution of an economic variable at a given horizon, as a function of a set of factors. These density forecasts are then be used to produce coherent forecasts for any downside risk measure, e.g., value-at-risk, expected shortfall, downside entropy. Initially introduced by Adrian et al. (2019) <doi:10.1257/aer.20161923> to reveal the vulnerability of economic growth to financial conditions, the MaR approach is currently extensively used by international financial institutions to provide Value-at-Risk (VaR) type forecasts for GDP growth (Growth-at-Risk) or inflation (Inflation-at-Risk). This package provides methods for estimating these models. Datasets for the US and the Eurozone are available to allow testing of the Adrian et al (2019) model. This package constitutes a useful toolbox (data and functions) for private practitioners, scholars as well as policymakers.
Depends: R (≥ 2.10)
License: GPL-3
Encoding: UTF-8
RoxygenNote: 7.2.3
Imports: stats, quantreg, sn, dfoptim, plot3D
NeedsCompilation: no
Packaged: 2023-04-28 21:12:07 UTC; quentin.lajaunie_ver
Author: Quentin Lajaunie [aut, cre], Guillaume Flament [aut], Christophe Hurlin [aut]
Maintainer: Quentin Lajaunie <quentin_lajaunie@hotmail.fr>
Repository: CRAN
Date/Publication: 2023-05-02 08:30:05 UTC

Historical data for the US (GDP and Financial Conditions) from 1973:Q1 to 2022:Q3

Description

data_euro contains: - Quarterly annualized GDP, from 1973:Q1 to 2022:Q3 - National Financial Condition Index of the US, from 1973:Q1 to 2022:Q3 Sources : https://www.chicagofed.org/research/data/nfci/current-data https://fred.stlouisfed.org/series/A191RL1Q225SBEA

Usage

data("data_US")

Format

A data frame with 200 observations on the following 4 variables.

DATE

Vector of dates.

GDP

Vector of annualized PIB.

NFCI

Historical values of the National Financial Condition Index (NFCI).

Historical data for the eurozone (GDP and Financial Conditions) from 2008:Q4 to 2022:Q3

Description

data_euro contains: - Quarterly annualized GDP, from 2008:Q4 to 2022:Q3 - Financial Condition Index of the euro Area, from 2008:Q4 to 2022:Q3 - Composite Indicator of Systemic Stress, from 2008:Q4 to 2022:Q3 Sources : https://sdw.ecb.europa.eu/browseExplanation.do?node=9689686 https://webstat.banque-france.fr/ws_wsen/browseSelection.do?node=DATASETS_FCI https://fred.stlouisfed.org/series/CLVMEURSCAB1GQEA19

Usage

data("data_euro")

Format

A data frame with 57 observations on the following 4 variables.

DATE

Vector of dates.

GDP

Vector of annualized PIB.

FCI

Historical values of the Financial Condition Index (FCI).

CISS

Historical values of the Composite Indicator of Systemic Stress (CISS).

Expected Shortfall

Description

The function allows to calculate Expected-shortfall for a given distribution. It takes as parameters alpha (risk level), a distribution and the parameters associated with this distribution. For example, for a normal distribution, the user must enter the mean and the standard deviation. Currently, the function can calculate the Expected-shortfall for the normal distribution and for the skew-t distribution (Azzalini and Capitianio, 2003)

Usage

f_ES(alpha, dist, params, accuracy = 1e-05)

Arguments

alpha

Numeric argument for Expected-Shortfall, between 0 and 1

dist

String for the type of distribution (gaussian or skew-t)

params

Numeric vector containing parameters of the distribution

accuracy

Scalar value which regulates the accuracy of the ES (default value 1e-05)

Value

Numeric value for the expected-shortfall given the distribution and the alpha risk

References

Azzalini, Adelchi, and Antonella Capitanio. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65.2 (2003): 367-389.

Azzalini, Adelchi, and Maintainer Adelchi Azzalini. "Package ‘sn’." The skew-normal and skew-t distributions (2015): 1-3.

Examples

f_ES(0.95, "gaussian", params=c(0,1))
f_ES(0.95, "gaussian", params=c(0,1), accuracy=1e-05)
f_ES(0.95, "gaussian", params=c(0,1), accuracy=1e-04)

Value-at-Risk

Description

The function allows to calculate Value-at-Risk for a given distribution. It takes as parameters alpha (risk level), a distribution and the parameters associated with this distribution. For example, for a normal distribution, the user must enter the mean and the standard deviation. Currently, the function can calculate the Value-at-Risk for the normal distribution and for the skew-t distribution (Azzalini and Capitianio, 2003)

Usage

f_VaR(alpha, dist, params)

Arguments

alpha

Numeric argument for Expected-Shortfall, between 0 and 1

dist

String for the type of distribution (gaussian or skew-t)

params

Numeric vector containing parameters of the distribution

Value

Numeric value for the Value-at-Risk given the distribution and the alpha risk

References

Azzalini, Adelchi, and Antonella Capitanio. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 65.2 (2003): 367-389.

Azzalini, Adelchi, and Maintainer Adelchi Azzalini. "Package ‘sn’." The skew-normal and skew-t distributions (2015): 1-3.

Examples

f_VaR(0.95, "gaussian", params=c(0,1))

Estimation of quantiles

Description

Predicted values based on each quantile regression (Koenker and Basset, 1978), at time=t_trgt, for each quantile in qt_trgt.

Usage

f_compile_quantile(qt_trgt, v_dep, v_expl, t_trgt)

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)

t_trgt

Numeric time target (optional)

Value

Numeric matrix with the predicted values based on each quantile regression, at time fixed in input

References

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

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)),]

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),
t_trgt = 30)

Distribution

Description

This function is used to estimate the parameters of the distribution (mean and standard deviation for Gaussian, xi, omega, alpha, and nu for skew-t) 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)

Arguments

type_function

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

compile_qt

Numeric matrix containing different quantiles and associated values

starting_values

Numeric vector with initial values for optimization

Value

a data.frame with the parameters of the distribution

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.

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)),]

# 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),
t_trgt = 30)

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),
t_trgt = 30)

results_s <- f_distrib(type_function="skew-t",
compile_qt=results_quantile_reg,
starting_values=c(0, 1, -0.5, 1.3))

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)