| Title: | Macroeconomic-at-Risk |
|---|---|
| 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. |
| Authors: | Quentin Lajaunie [aut, cre], Guillaume Flament [aut], Christophe Hurlin [aut] |
| Maintainer: | Quentin Lajaunie <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-12-18 06:32:06 UTC |
| Source: | CRAN |
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
data("data_euro")data("data_euro")
A data frame with 57 observations on the following 4 variables.
DATEVector of dates.
GDPVector of annualized PIB.
FCIHistorical values of the Financial Condition Index (FCI).
CISSHistorical values of the Composite Indicator of Systemic Stress (CISS).
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
data("data_US")data("data_US")
A data frame with 200 observations on the following 4 variables.
DATEVector of dates.
GDPVector of annualized PIB.
NFCIHistorical values of the National Financial Condition Index (NFCI).
Predicted values based on each quantile regression (Koenker and Basset, 1978), at time=t_trgt, for each quantile in qt_trgt.
f_compile_quantile(qt_trgt, v_dep, v_expl, t_trgt)f_compile_quantile(qt_trgt, v_dep, v_expl, t_trgt)
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) |
Numeric matrix with the predicted values based on each quantile regression, at time fixed in input
Koenker, Roger, and Gilbert Bassett Jr. "Regression quantiles." Econometrica: journal of the Econometric Society (1978): 33-50.
# 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)# 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)
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.
f_distrib(type_function, compile_qt, starting_values)f_distrib(type_function, compile_qt, starting_values)
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 |
a data.frame with the parameters of the distribution
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.
# 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))# 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))
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.
f_distrib_histo( qt_trgt, v_dep, v_expl, type_function, starting_values, step, x_min, x_max )f_distrib_histo( qt_trgt, v_dep, v_expl, type_function, starting_values, step, x_min, x_max )
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) |
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 |
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.
# 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$distrib_histo[,2], pch = 10, theta = 70, phi = 10, main = "Distribution of GDP Growth over time - Euro Area", xlab = "Date", ylab ="Pib", zlab="", cex = 0.3)# Import data data("data_euro") # Data process PIB_euro_forward_4 = data_euro["GDP"][c(5:length(data_euro["GDP"][,1])),] FCI_euro_lag_4 = data_euro["FCI"][c(1:(length(data_euro["GDP"][,1]) - 4)),] CISS_euro_lag_4 = data_euro["CISS"][c(1:(length(data_euro["GDP"][,1]) - 4)),] results_histo <- f_distrib_histo(qt_trgt=c(0.10,0.25,0.75,0.90), v_dep=PIB_euro_forward_4, v_expl=cbind(FCI_euro_lag_4,CISS_euro_lag_4), type_function="skew-t", starting_values=c(0, 1, -0.5, 1.3), step=5, x_min=-10, x_max=5) library(plot3D) # load scatter3D(results_histo$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)
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)
f_ES(alpha, dist, params, accuracy = 1e-05)f_ES(alpha, dist, params, accuracy = 1e-05)
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) |
Numeric value for the expected-shortfall given the distribution and the alpha risk
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.
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)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)
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)
f_VaR(alpha, dist, params)f_VaR(alpha, dist, params)
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 |
Numeric value for the Value-at-Risk given the distribution and the alpha risk
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.
f_VaR(0.95, "gaussian", params=c(0,1))f_VaR(0.95, "gaussian", params=c(0,1))