Package 'bayesianVARs'

Title:	MCMC Estimation of Bayesian Vectorautoregressions
Description:	Efficient Markov Chain Monte Carlo (MCMC) algorithms for the fully Bayesian estimation of vectorautoregressions (VARs) featuring stochastic volatility (SV). Implements state-of-the-art shrinkage priors following Gruber & Kastner (2023) <doi:10.48550/arXiv.2206.04902>. Efficient equation-per-equation estimation following Kastner & Huber (2020) <doi:10.1002/for.2680> and Carrerio et al. (2021) <doi:10.1016/j.jeconom.2021.11.010>.
Authors:	Luis Gruber [cph, aut, cre] , Gregor Kastner [ctb]
Maintainer:	Luis Gruber <[email protected]>
License:	GPL (>= 3)
Version:	0.1.5
Built:	2024-11-13 22:16:47 UTC
Source:	https://github.com/luisgruber/bayesianvars

Help Index

Extract or Replace Parts of a bayesianVARs_coef object
Extract or Replace Parts of a bayesianVARs_draws object
Markov Chain Monte Carlo Sampling for Bayesian Vectorautoregressions
Extract VAR coefficients
Simulate fitted/predicted historical values for an estimated VAR model
Draw from generalized inverse Gaussian
Pairwise visualization of out-of-sample posterior predictive densities.
Plot method for bayesianVARs_bvar
Visualization of in-sample fit of an estimated VAR.
Fan chart
Posterior heatmaps for VAR coefficients or variance-covariance matrices
Predict method for Bayesian VARs
Pretty printing of a bvar object
Print method for bayesianVARs_predict objects
Print method for summary.bayesianVARs_bvar objects
Print method for summary.bayesianVARs_predict objects
Specify prior on PHI
Specify prior on Sigma
Stable posterior draws
Summary method for bayesianVARs_bvar objects
Summary statistics for bayesianVARs posterior draws.
Summary method for bayesianVARs_predict objects
Data from the US-economy
Extract posterior draws of the (time-varying) variance-covariance matrix for a VAR model

Extract or Replace Parts of a bayesianVARs_coef object

Description

Extract or replace parts of a bayesianVARs_coef object.

Usage

## S3 method for class 'bayesianVARs_coef'
x[i, j, ...]
## S3 method for class 'bayesianVARs_coef'
x[i, j, ...]

Arguments

`x`	An object of type `bayesianVARs_coef`.
`i`	indices
`j`	indices
`...`	further indices

Value

An object of type bayesianVARs_coef.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract coefficients, which are of class bayesianVARs_coef
phi <- coef(mod)
phi[1,1,1]
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract coefficients, which are of class bayesianVARs_coef
phi <- coef(mod)
phi[1,1,1]

Extract or Replace Parts of a bayesianVARs_draws object

Description

Extract or replace parts of a bayesianVARs_draws object.

Usage

## S3 method for class 'bayesianVARs_draws'
x[i, j, ...]
## S3 method for class 'bayesianVARs_draws'
x[i, j, ...]

Arguments

`x`	An object of type `bayesianVARs_draws`.
`i`	indices
`j`	indices
`...`	further indices

Value

An object of type bayesianVARs_draws.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract coefficients, which are of class bayesianVARs_draws
phi <- coef(mod)
phi[1,1,1]
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract coefficients, which are of class bayesianVARs_draws
phi <- coef(mod)
phi[1,1,1]

Markov Chain Monte Carlo Sampling for Bayesian Vectorautoregressions

Description

bvar simulates from the joint posterior distribution of the parameters and latent variables and returns the posterior draws.

Usage

bvar(
  data,
  lags = 1L,
  draws = 1000L,
  burnin = 1000L,
  thin = 1L,
  prior_intercept = 10,
  prior_phi = specify_prior_phi(data = data, lags = lags, prior = "HS"),
  prior_sigma = specify_prior_sigma(data = data, type = "factor", quiet = TRUE),
  sv_keep = "last",
  quiet = FALSE,
  startvals = list(),
  expert = list()
)
bvar(
  data,
  lags = 1L,
  draws = 1000L,
  burnin = 1000L,
  thin = 1L,
  prior_intercept = 10,
  prior_phi = specify_prior_phi(data = data, lags = lags, prior = "HS"),
  prior_sigma = specify_prior_sigma(data = data, type = "factor", quiet = TRUE),
  sv_keep = "last",
  quiet = FALSE,
  startvals = list(),
  expert = list()
)

Arguments

`data`	Data matrix (can be a time series object). Each of $M$ columns is assumed to contain a single time-series of length $T$ .
`lags`	Integer indicating the order of the VAR, i.e. the number of lags of the dependent variables included as predictors.
`draws`	single integer indicating the number of draws after the burnin
`burnin`	single integer indicating the number of draws discarded as burnin
`thin`	single integer. Every $thin$ th draw will be stored. Default is `thin=1L`.
`prior_intercept`	Either `prior_intercept=FALSE` and no constant term (intercept) will be included. Or a numeric vector of length $M$ indicating the (fixed) prior standard deviations on the constant term. A single number will be recycled accordingly. Default is `prior_intercept=10`.
`prior_phi`	`bayesianVARs_prior_phi` object specifying prior for the reduced form VAR coefficients. Best use constructor `specify_prior_phi`.
`prior_sigma`	`bayesianVARs_prior_sigma` object specifying prior for the variance-covariance matrix of the VAR. Best use constructor `specify_prior_sigma`.
`sv_keep`	String equal to `"all"` or `"last"`. In case of `sv_keep = "last"`, the default, only draws for the very last log-variance $h_T$ are stored.
`quiet`	logical value indicating whether information about the progress during sampling should be displayed during sampling (default is `TRUE`).
`startvals`	optional list with starting values.
`expert`	optional list with expert settings.

Details

The VAR(p) model is of the following form: $\boldsymbol{y}^\prime_t = \boldsymbol{\iota}^\prime + \boldsymbol{x}^\prime_t\boldsymbol{\Phi} + \boldsymbol{\epsilon}^\prime_t$ , where $\boldsymbol{y}_t$ is a $M$ -dimensional vector of dependent variables and $\boldsymbol{\epsilon}_t$ is the error term of the same dimension. $\boldsymbol{x}_t$ is a $K=pM$ -dimensional vector containing lagged/past values of the dependent variables $\boldsymbol{y}_{t-l}$ for $l=1,\dots,p$ and $\boldsymbol{\iota}$ is a constant term (intercept) of dimension $M\times 1$ . The reduced-form coefficient matrix $\boldsymbol{\Phi}$ is of dimension $K \times M$ .

bvar offers two different specifications for the errors: The user can choose between a factor stochastic volatility structure or a cholesky stochastic volatility structure. In both cases the disturbances $\boldsymbol{\epsilon}_t$ are assumed to follow a $M$ -dimensional multivariate normal distribution with zero mean and variance-covariance matrix $\boldsymbol{\Sigma}_t$ . In case of the cholesky specification $\boldsymbol{\Sigma}_t = \boldsymbol{U}^{\prime -1} \boldsymbol{D}_t \boldsymbol{U}^{-1}$ , where $\boldsymbol{U}^{-1}$ is upper unitriangular (with ones on the diagonal). The diagonal matrix $\boldsymbol{D}_t$ depends upon latent log-variances, i.e. $\boldsymbol{D}_t=diag(exp(h_{1t}),\dots, exp(h_{Mt})$ . The log-variances follow a priori independent autoregressive processes $h_{it}\sim N(\mu_i + \phi_i(h_{i,t-1}-\mu_i),\sigma_i^2)$ for $i=1,\dots,M$ . In case of the factor structure, $\boldsymbol{\Sigma}_t = \boldsymbol{\Lambda} \boldsymbol{V}_t \boldsymbol{\Lambda}^\prime + \boldsymbol{G}_t$ . The diagonal matrices $\boldsymbol{V}_t$ and $\boldsymbol{G}_t$ depend upon latent log-variances, i.e. $\boldsymbol{G}_t=diag(exp(h_{1t}),\dots, exp(h_{Mt})$ and $\boldsymbol{V}_t=diag(exp(h_{M+1,t}),\dots, exp(h_{M+r,t})$ . The log-variances follow a priori independent autoregressive processes $h_{it}\sim N(\mu_i + \phi_i(h_{i,t-1}-\mu_i),\sigma_i^2)$ for $i=1,\dots,M$ and $h_{M+j,t}\sim N(\phi_ih_{M+j,t-1},\sigma_{M+j}^2)$ for $j=1,\dots,r$ .

Value

An object of type bayesianVARs_bvar, a list containing the following objects:

PHI: A bayesianVARs_coef object, an array, containing the posterior draws of the VAR coefficients (including the intercept).
U: A bayesianVARs_draws object, a matrix, containing the posterior draws of the contemporaneous coefficients (if cholesky decomposition for sigma is specified).
logvar: A bayesianVARs_draws object containing the log-variance draws.
sv_para: A baysesianVARs_draws object containing the posterior draws of the stochastic volatility related parameters.
phi_hyperparameter: A matrix containing the posterior draws of the hyperparameters of the conditional normal prior on the VAR coefficients.
u_hyperparameter: A matrix containing the posterior draws of the hyperparameters of the conditional normal prior on U (if cholesky decomposition for sigma is specified).
bench: Numerical indicating the average time it took to generate one single draw of the joint posterior distribution of all parameters.
V_prior: An array containing the posterior draws of the variances of the conditional normal prior on the VAR coefficients.
facload: A bayesianVARs_draws object, an array, containing draws from the posterior distribution of the factor loadings matrix (if factor decomposition for sigma is specified).
fac: A bayesianVARs_draws object, an array, containing factor draws from the posterior distribution (if factor decomposition for sigma is specified).
Y: Matrix containing the dependent variables used for estimation.
X matrix containing the lagged values of the dependent variables, i.e. the covariates.
lags: Integer indicating the lag order of the VAR.
intercept: Logical indicating whether a constant term is included.
heteroscedastic logical indicating whether heteroscedasticity is assumed.
Yraw: Matrix containing the dependent variables, including the initial 'lags' observations.
Traw: Integer indicating the total number of observations.
sigma_type: Character specifying the decomposition of the variance-covariance matrix.
datamat: Matrix containing both 'Y' and 'X'.
config: List containing information on configuration parameters.

MCMC algorithm

To sample efficiently the reduced-form VAR coefficients assuming a factor structure for the errors, the equation per equation algorithm in Kastner & Huber (2020) is implemented. All parameters and latent variables associated with the factor-structure are sampled using package factorstochvol-package's function update_fsv callable on the C-level only.

To sample efficiently the reduced-form VAR coefficients, assuming a cholesky-structure for the errors, the corrected triangular algorithm in Carriero et al. (2021) is implemented. The SV parameters and latent variables are sampled using package stochvol's update_fast_sv function. The precision parameters, i.e. the free off-diagonal elements in $\boldsymbol{U}$ , are sampled as in Cogley and Sargent (2005).

References

Gruber, L. and Kastner, G. (2023). Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends! arXiv:2206.04902.

Kastner, G. and Huber, F. Sparse (2020). Bayesian vector autoregressions in huge dimensions. Journal of Forecasting. 39, 1142–1165, doi:10.1002/for.2680.

Kastner, G. (2019). Sparse Bayesian Time-Varying Covariance Estimation in Many Dimensions Journal of Econometrics, 210(1), 98–115, doi:10.1016/j.jeconom.2018.11.007.

Carriero, A. and Chan, J. and Clark, T. E. and Marcellino, M. (2021). Corrigendum to “Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors” [J. Econometrics 212 (1) (2019) 137–154]. Journal of Econometrics, doi:10.1016/j.jeconom.2021.11.010.

Cogley, S. and Sargent, T. (2005). Drifts and volatilities: monetary policies and outcomes in the post WWII US. Review of Economic Dynamics, 8, 262–302, doi:10.1016/j.red.2004.10.009.

Hosszejni, D. and Kastner, G. (2021). Modeling Univariate and Multivariate Stochastic Volatility in R with stochvol and factorstochvol. Journal of Statistical Software, 100, 1–-34. doi:10.18637/jss.v100.i12.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Plot
plot(mod)

# Summary
summary(mod)

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Plot
plot(mod)

# Summary
summary(mod)

Extract VAR coefficients

Description

Extracts posterior draws of the VAR coefficients from a VAR model estimated with bvar().

Usage

## S3 method for class 'bayesianVARs_bvar'
coef(object, ...)
## S3 method for class 'bayesianVARs_bvar'
coef(object, ...)

Arguments

`object`	A `bayesianVARs_bvar` object obtained from `bvar()`.
`...`	Currently ignored.

Value

Returns a numeric array of dimension $M \times K \times draws$ , where M is the number of time-series, K is the number of covariates per equation (including the intercept) and draws is the number of stored posterior draws.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of VAR coefficients
bvar_coefs <- coef(mod)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of VAR coefficients
bvar_coefs <- coef(mod)

Simulate fitted/predicted historical values for an estimated VAR model

Description

Simulates the fitted/predicted (in-sample) values for an estimated VAR model.

Usage

## S3 method for class 'bayesianVARs_bvar'
fitted(object, error_term = TRUE, ...)
## S3 method for class 'bayesianVARs_bvar'
fitted(object, error_term = TRUE, ...)

Arguments

`object`	A `bayesianVARs_bvar` object estimated via `bvar()`.
`error_term`	logical indicating whether to include the error term or not.
`...`	Currently ignored.

Value

An object of class bayesianVARs_fitted.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate predicted historical values including the error term.
pred <- fitted(mod, error_term = TRUE)

# Simulate fitted historical values not including the error term.
fit <- fitted(mod, error_term = FALSE)

# Visualize
plot(pred)
plot(fit)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate predicted historical values including the error term.
pred <- fitted(mod, error_term = TRUE)

# Simulate fitted historical values not including the error term.
fit <- fitted(mod, error_term = FALSE)

# Visualize
plot(pred)
plot(fit)

Draw from generalized inverse Gaussian

Description

Vectorized version of rgig

Usage

my_gig(n, lambda, chi, psi)
my_gig(n, lambda, chi, psi)

Arguments

`n`	A single integer indicating the number of draws to generate.
`lambda`	vector of shape parameters.
`chi`	vector of shape/scale parameters. Must be nonnegative for positive lambdas and positive else.
`psi`	vector of shape/scale parameters. Must be nonnegative for negative lambdas and positive else.

Value

Matrix of dimension c(n,m), where m is the maximum length of lambda, psi and chi.

Examples

gigsamples <- my_gig(2, c(1,1), c(1,1), c(1,1))
gigsamples <- my_gig(2, c(1,1), c(1,1), c(1,1))

Pairwise visualization of out-of-sample posterior predictive densities.

Description

Pairwise visualization of out-of-sample posterior predictive densities.

Usage

## S3 method for class 'bayesianVARs_predict'
pairs(x, vars, ahead, ...)
## S3 method for class 'bayesianVARs_predict'
pairs(x, vars, ahead, ...)

Arguments

`x`	An object of class `bayesianVARs_predict` obtained via `predict.bayesianVARs_bvar()`.
`vars`	Integer vector (or coercible to such) indicating which variables to plot.
`ahead`	Integer vector (or coercible to such) indicating which step ahead to plot. `max(ahead)` must be smaller equal to `dim(x$predictions)[1]`.
`...`	Currently ignored!

Value

Returns x invisibly.

Note

Note that that bayesianVARs_predict can also be used withing plot.bayesianVARs_bvar().

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate from posterior predictive
predictions <- predict(mod, ahead = 1:3)

# Visualize
pairs(predictions, vars = 1:3, ahead = 1:3)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate from posterior predictive
predictions <- predict(mod, ahead = 1:3)

# Visualize
pairs(predictions, vars = 1:3, ahead = 1:3)

Plot method for bayesianVARs_bvar

Description

Visualization of in-sample fit. Can also be used to display prediction intervals of future values.

Usage

## S3 method for class 'bayesianVARs_bvar'
plot(
  x,
  predictions = NULL,
  quantiles = c(0.05, 0.5, 0.95),
  dates = NULL,
  n_col = 1,
  ...
)
## S3 method for class 'bayesianVARs_bvar'
plot(
  x,
  predictions = NULL,
  quantiles = c(0.05, 0.5, 0.95),
  dates = NULL,
  n_col = 1,
  ...
)

Arguments

`x`	An object of class `bayesianVARs_bvar` obtained via `bvar()`.
`predictions`	Optional array of out of sample predictions, e.g. obtained via `predict.bayesianVARs_bvar()`.
`quantiles`	numeric vector indicating which quantiles to plot.
`dates`	optional vector of dates for labelling the x-axis. The default values is `NULL`; in this case, the axis will be labeled with numbers.
`n_col`	integer indicating the number of columns to use for plotting.
`...`	Currently ignored!

Value

Returns x invisibly.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate from posterior predictive
predictions <- predict(mod, ahead = 1:3)

# Visualize
plot(mod, predictions = predictions)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate from posterior predictive
predictions <- predict(mod, ahead = 1:3)

# Visualize
plot(mod, predictions = predictions)

Visualization of in-sample fit of an estimated VAR.

Description

Visualization of in-sample fit of an estimated VAR.

Usage

## S3 method for class 'bayesianVARs_fitted'
plot(
  x,
  dates = NULL,
  vars = "all",
  quantiles = c(0.05, 0.5, 0.95),
  n_col = 1L,
  ...
)
## S3 method for class 'bayesianVARs_fitted'
plot(
  x,
  dates = NULL,
  vars = "all",
  quantiles = c(0.05, 0.5, 0.95),
  n_col = 1L,
  ...
)

Arguments

`x`	A `bayesianVARs_fitted` object.
`dates`	optional vector of dates for labelling the x-axis. The default values is `NULL`; in this case, the axis will be labeled with numbers.
`vars`	character vector containing the names of the variables to be visualized. The default is `"all"` indicating that the fit of all variables is visualized.
`quantiles`	numeric vector indicating which quantiles to plot.
`n_col`	integer indicating the number of columns to use for plotting.
`...`	Currently ignored.

Value

returns x invisibly

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate predicted historical values including the error term.
pred <- fitted(mod, error_term = TRUE)

# Visualize
plot(pred)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate predicted historical values including the error term.
pred <- fitted(mod, error_term = TRUE)

# Visualize
plot(pred)

Fan chart

Description

Visualization of (out-of-sample) predictive distribution.

Usage

## S3 method for class 'bayesianVARs_predict'
plot(
  x,
  dates = NULL,
  vars = "all",
  ahead = NULL,
  quantiles = c(0.05, 0.25, 0.5, 0.75, 0.95),
  n_col = 1L,
  first_obs = 1L,
  ...
)
## S3 method for class 'bayesianVARs_predict'
plot(
  x,
  dates = NULL,
  vars = "all",
  ahead = NULL,
  quantiles = c(0.05, 0.25, 0.5, 0.75, 0.95),
  n_col = 1L,
  first_obs = 1L,
  ...
)

Arguments

`x`	An object of type `bayesianVARs_predict` obtained via `predict.bayesianVARs_bvar()`.
`dates`	optional vector of dates for labeling the x-axis. The default values is `NULL`; in this case, the axis will be labeled with numbers.
`vars`	character vector containing the names of the variables to be visualized. The default is `"all"` indicating that all variables are visualized.
`ahead`	Integer vector (or coercible to such) indicating which step ahead to plot. `max(ahead)` must be smaller equal to `dim(x$predictions)[1]`.
`quantiles`	numeric vector indicating which quantiles to plot.
`n_col`	integer indicating the number of columns to use for plotting.
`first_obs`	integer indicating the first observation to be used for plotting.
`...`	Currently ignored!

Value

Returns x invisibly!

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate from posterior predictive
predictions <- predict(mod, ahead = 1:3)

# Visualize
plot(predictions, vars = 1:3, ahead = 1:3)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Simulate from posterior predictive
predictions <- predict(mod, ahead = 1:3)

# Visualize
plot(predictions, vars = 1:3, ahead = 1:3)

Posterior heatmaps for VAR coefficients or variance-covariance matrices

Description

Posterior heatmaps for VAR coefficients or variance-covariance matrices

Usage

posterior_heatmap(
  x,
  FUN,
  ...,
  colorbar = TRUE,
  xlabels = NULL,
  ylabels = NULL,
  add_numbers = FALSE,
  zlim = NULL,
  colspace = NULL,
  main = "",
  cex.axis = 0.75,
  cex.colbar = 1,
  cex.numbers = 1,
  asp = NULL
)
posterior_heatmap(
  x,
  FUN,
  ...,
  colorbar = TRUE,
  xlabels = NULL,
  ylabels = NULL,
  add_numbers = FALSE,
  zlim = NULL,
  colspace = NULL,
  main = "",
  cex.axis = 0.75,
  cex.colbar = 1,
  cex.numbers = 1,
  asp = NULL
)

Arguments

`x`	An array of dimension $a \times b \times draws$ , where $a \times b$ is the dimension of the parameter to visualize and draws is the number of posterior draws.
`FUN`	The summary function to be applied to margins `c(1,2)` of x. E.g. `"median"`, `"mean"`, `"IQR"`, `"sd"` or `"var"`. `apply(x, 1:2, FUN, ...)` must return a matrix!
`...`	optional arguments to `FUN`.
`colorbar`	logical indicating whether to display a colorbar or not. Default is `TRUE`.
`xlabels`	`ylabels=NULL`, the default, indicates that the names of the dependent variables will be displayed. `ylabels=""` indicates that no ylabels will be displayed.
`ylabels`	`xlabels=NULL`, the default, indicates that the labels of all covariables (the lagged values of the dependent variables) will be displayed. `xlabels="lags"` indicates that only the lags will be marked. `xlabels=""` indicates that no ylabels are displayed.
`add_numbers`	logical. `add_numbers=TRUE`, the default indicates that the actual values of `summary` will be displayed.
`zlim`	numeric vector of length two indicating the minimum and maximum values for which colors should be plotted. By default this range is determined by the maximum of the absolute values of the selected summary.
`colspace`	Optional argument.
`main`	main title for the plot.
`cex.axis`	The magnification to be used for y-axis annotation relative to the current setting of cex.
`cex.colbar`	The magnification to be used for colorbar annotation relative to the current setting of cex.
`cex.numbers`	The magnification to be used for the actual values (if `add_numbers=TRUE`) relative to the current setting of cex.
`asp`	aspect ratio.

Value

Returns x invisibly.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(100*data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of VAR coefficients
phi_post <- coef(mod)

# Visualize posterior median of VAR coefficients
posterior_heatmap(phi_post, median)

# Extract posterior draws of variance-covariance matrices (for each point in time)
sigma_post <- vcov(mod)
# Visualize posterior interquartile-range of variance-covariance matrix of the first observation
posterior_heatmap(sigma_post[1,,,], IQR)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(100*data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of VAR coefficients
phi_post <- coef(mod)

# Visualize posterior median of VAR coefficients
posterior_heatmap(phi_post, median)

# Extract posterior draws of variance-covariance matrices (for each point in time)
sigma_post <- vcov(mod)
# Visualize posterior interquartile-range of variance-covariance matrix of the first observation
posterior_heatmap(sigma_post[1,,,], IQR)

Predict method for Bayesian VARs

Description

Simulates from (out-of-sample) predictive density for Bayesian VARs estimated via bvar() and computes log predictive likelhoods if ex-post observed data is supplied.

Usage

## S3 method for class 'bayesianVARs_bvar'
predict(
  object,
  ahead = 1L,
  each = 1L,
  stable = TRUE,
  simulate_predictive = TRUE,
  LPL = FALSE,
  Y_obs = NA,
  LPL_VoI = NA,
  ...
)
## S3 method for class 'bayesianVARs_bvar'
predict(
  object,
  ahead = 1L,
  each = 1L,
  stable = TRUE,
  simulate_predictive = TRUE,
  LPL = FALSE,
  Y_obs = NA,
  LPL_VoI = NA,
  ...
)

Arguments

`object`	A `bayesianVARs_bvar` object, obtained from `bvar()`.
`ahead`	Integer vector (or coercible to such), indicating the number of steps ahead at which to predict.
`each`	Single integer (or coercible to such) indicating how often should be drawn from the posterior predictive distribution for each draw that has been stored during MCMC sampling.
`stable`	logical indicating whether to consider only those draws from the posterior that fulfill the 'stable' criterion. Default is `TRUE`.
`simulate_predictive`	logical, indicating whether the posterior predictive distribution should be simulated.
`LPL`	logical indicating whether `ahead`-step-ahead log predictive likelihoods should be computed. If `LPL=TRUE`, `Y_obs` has to be specified.
`Y_obs`	Data matrix of observed values for computation of log predictive likelihood. Each of `ncol(object$Yraw)` columns is assumed to contain a single time-series of length `length(ahead)`.
`LPL_VoI`	either integer vector or character vector of column-names indicating for which subgroup of time-series in `object$Yraw` a joint log predictive likelihood shall be computed.
`...`	Currently ignored!

Value

Object of class bayesianVARs_predict, a list that may contain the following elements:

predictions array of dimensions c(length(ahead), ncol(object$Yraw), each * dim(object$PHI)[3]) containing the simulations from the predictive density (if simulate_predictive=TRUE).
LPL vector of length length(ahead) containing the log-predictive-likelihoods (taking into account the joint distribution of all variables) (if LPL=TRUE).
LPL_univariate matrix of dimension ⁠c(length(ahead), ncol(object$Yraw)⁠ containing the marginalized univariate log-predictive-likelihoods of each series (if LPL=TRUE).
LPL_VoI vector of length length(ahead) containing the log-predictive-likelihoods for a subset of variables (if LPL=TRUE and LPL_VoI != NA).
Yraw matrix containing the data used for the estimation of the VAR.
LPL_draws matrix containing the simulations of the log-predictive-likelihood (if LPL=TRUE).
PL_univariate_draws array containing the simulations of the univariate predictive-likelihoods (if LPL=TRUE).
LPL_sub_draws matrix containing the simulations of the log-predictive-likelihood for a subset of variables (if LPL=TRUE and LPL_VoI != NA).

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step to 4-steps ahead posterior predictive and compute
# log-predictive-likelihoods
predictions <- predict(mod, ahead = 1:4, LPL = TRUE, Y_obs = test)

# Summary
summary(predictions)

# Visualize via fan-charts
plot(predictions)


# In order to evaluate the joint predictive density of a subset of the
# variables (variables of interest), consider specifying 'LPL_VoI':
predictions <- predict(mod, ahead = 1:4, LPL = TRUE, Y_obs = test, LPL_VoI = c("GDPC1","FEDFUNDS"))
predictions$LPL_VoI

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step to 4-steps ahead posterior predictive and compute
# log-predictive-likelihoods
predictions <- predict(mod, ahead = 1:4, LPL = TRUE, Y_obs = test)

# Summary
summary(predictions)

# Visualize via fan-charts
plot(predictions)


# In order to evaluate the joint predictive density of a subset of the
# variables (variables of interest), consider specifying 'LPL_VoI':
predictions <- predict(mod, ahead = 1:4, LPL = TRUE, Y_obs = test, LPL_VoI = c("GDPC1","FEDFUNDS"))
predictions$LPL_VoI

Pretty printing of a bvar object

Description

Pretty printing of a bvar object

Usage

## S3 method for class 'bayesianVARs_bvar'
print(x, ...)
## S3 method for class 'bayesianVARs_bvar'
print(x, ...)

Arguments

`x`	Object of class `bayesianVARs_bvar`, usually resulting from a call of `bvar()`.
`...`	Ignored.

Value

Returns x invisibly.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Print model
mod

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Print model
mod

Print method for bayesianVARs_predict objects

Description

Print method for bayesianVARs_predict objects.

Usage

## S3 method for class 'bayesianVARs_predict'
print(x, ...)
## S3 method for class 'bayesianVARs_predict'
print(x, ...)

Arguments

`x`	A `bayesianVARs_predict` object obtained via `predict.bayesianVARs_bvar()`.
`...`	Currently ignored!

Value

Returns x invisibly.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step ahead posterior predictive
predictions <- predict(mod, ahead = 1L)
print(predictions)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step ahead posterior predictive
predictions <- predict(mod, ahead = 1L)
print(predictions)

Print method for summary.bayesianVARs_bvar objects

Description

Print method for summary.bayesianVARs_bvar objects.

Usage

## S3 method for class 'summary.bayesianVARs_bvar'
print(x, ...)
## S3 method for class 'summary.bayesianVARs_bvar'
print(x, ...)

Arguments

`x`	A `summary.bayesianVARs_bvar` object obtained via `summary.bayesianVARs_bvar()`.
`...`	Currently ignored!

Value

Returns x invisibly!

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate model
mod <- bvar(data, quiet = TRUE)

# Print summary
summary(mod)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate model
mod <- bvar(data, quiet = TRUE)

# Print summary
summary(mod)

Print method for summary.bayesianVARs_predict objects

Description

Print method for summary.bayesianVARs_predict objects.

Usage

## S3 method for class 'summary.bayesianVARs_predict'
print(x, ...)
## S3 method for class 'summary.bayesianVARs_predict'
print(x, ...)

Arguments

`x`	A `summary.bayesianVARs_predict` object obtained via `summary.bayesianVARs_predict()`.
`...`	Currently ignored.

Value

Returns x invisibly.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step ahead posterior predictive
predictions <- predict(mod, ahead = 1L)
sum <- summary(predictions)
print(sum)

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step ahead posterior predictive
predictions <- predict(mod, ahead = 1L)
sum <- summary(predictions)
print(sum)

Specify prior on PHI

Description

Configures prior on PHI, the matrix of reduced-form VAR coefficients.

Usage

specify_prior_phi(
  data = NULL,
  M = ncol(data),
  lags = 1L,
  prior = "HS",
  priormean = 0,
  PHI_tol = 1e-18,
  DL_a = "1/K",
  DL_tol = 0,
  R2D2_a = 0.1,
  R2D2_b = 0.5,
  R2D2_tol = 0,
  NG_a = 0.1,
  NG_b = 1,
  NG_c = 1,
  NG_tol = 0,
  SSVS_c0 = 0.01,
  SSVS_c1 = 100,
  SSVS_semiautomatic = TRUE,
  SSVS_p = 0.5,
  HMP_lambda1 = c(0.01, 0.01),
  HMP_lambda2 = c(0.01, 0.01),
  normal_sds = 10,
  global_grouping = "global",
  ...
)
specify_prior_phi(
  data = NULL,
  M = ncol(data),
  lags = 1L,
  prior = "HS",
  priormean = 0,
  PHI_tol = 1e-18,
  DL_a = "1/K",
  DL_tol = 0,
  R2D2_a = 0.1,
  R2D2_b = 0.5,
  R2D2_tol = 0,
  NG_a = 0.1,
  NG_b = 1,
  NG_c = 1,
  NG_tol = 0,
  SSVS_c0 = 0.01,
  SSVS_c1 = 100,
  SSVS_semiautomatic = TRUE,
  SSVS_p = 0.5,
  HMP_lambda1 = c(0.01, 0.01),
  HMP_lambda2 = c(0.01, 0.01),
  normal_sds = 10,
  global_grouping = "global",
  ...
)

Arguments

`data`	Optional. Data matrix (can be a time series object). Each of $M$ columns is assumed to contain a single time-series of length $T$ .
`M`	positive integer indicating the number of time-series of the VAR.
`lags`	positive integer indicating the order of the VAR, i.e. the number of lags of the dependent variables included as predictors.
`prior`	character, one of `"HS"`, `"R2D2"`, `"NG"`, `"DL"`, `"SSVS"`, `"HMP"` or `"normal"`.
`priormean`	real numbers indicating the prior means of the VAR coefficients. One single number means that the prior mean of all own-lag coefficients w.r.t. the first lag equals `priormean` and `0` else. A vector of length M means that the prior mean of the own-lag coefficients w.r.t. the first lag equals `priormean` and `0` else. If `priormean` is a matrix of dimension `c(lagsM,M)`, then each of the $M$ columns is assumed to contain `lagsM` prior means for the VAR coefficients of the respective VAR equations.
`PHI_tol`	Minimum number that the absolute value of a VAR coefficient draw can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero.
`DL_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. If the argument `global_grouping` specifies e.g. `k` groups, then `DL_a` can be a numeric vector of length `k` and the elements indicate the shrinkage in each group. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains `s` support points and the second column contains the associated prior probabilities. `DL_a` has only to be specified if `prior="DL"`.
`DL_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the Dirichlet Laplace prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `DL_tol` has only to be specified if `prior="DL"`.
`R2D2_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. If the argument `global_grouping` specifies e.g. `k` groups, then `R2D2_a` can be a numeric vector of length `k` and the elements indicate the shrinkage in each group. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains `s` support points and the second column contains the associated prior probabilities. `R2D2_a` has only to be specified if `prior="R2D2"`.
`R2D2_b`	(Single) positive real number. The value indicates the shape parameter of the inverse gamma prior on the (semi-)global scales. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_b` can be a numeric vector of length `k` and the elements determine the shape parameter in each group. `R2D2_b` has only to be specified if `prior="R2D2"`.
`R2D2_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the R2D2 prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `R2D2_tol` has only to be specified if `prior="R2D2"`.
`NG_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_a` can be a numeric vector of length `k` and the elements indicate the shrinkage in each group. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains `s` support points and the second column contains the associated prior probabilities. `NG_a` has only to be specified if `prior="NG"`.
`NG_b`	(Single) positive real number. The value indicates the shape parameter of the inverse gamma prior on the (semi-)global scales. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_b` can be a numeric vector of length `k` and the elements determine the shape parameter in each group. `NG_b` has only to be specified if `prior="NG"`.
`NG_c`	(Single) positive real number. The value indicates the scale parameter of the inverse gamma prior on the (semi-)global scales. If the argument `global_grouping` specifies e.g. `k` groups, then `NG_c` can be a numeric vector of length `k` and the elements determine the scale parameter in each group. Expert option would be to set the scale parameter proportional to `NG_a`. E.g. in the case where a discrete hyperprior for `NG_a` is chosen, a desired proportion of let's say `0.2` is achieved by setting `NG_c="0.2*a"` (character input!). `NG_c` has only to be specified if `prior="NG"`.
`NG_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the normal-gamma prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `NG_tol` has only to be specified if `prior="NG"`.
`SSVS_c0`	single positive number indicating the (unscaled) standard deviation of the spike component. `SSVS_c0` has only to be specified if `prior="SSVS"`. It should be that $SSVS_{c0} \ll SSVS_{c1}$ ! `SSVS_c0` has only to be specified if `prior="SSVS"`.
`SSVS_c1`	single positive number indicating the (unscaled) standard deviation of the slab component. `SSVS_c0` has only to be specified if `prior="SSVS"`. It should be that $SSVS_{c0} \ll SSVS_{c1}$ !
`SSVS_semiautomatic`	logical. If `SSVS_semiautomatic=TRUE` both `SSVS_c0` and `SSVS_c1` will be scaled by the variances of the posterior of PHI under a FLAT conjugate (dependent Normal-Wishart prior). `SSVS_semiautomatic` has only to be specified if `prior="SSVS"`.
`SSVS_p`	Either a single positive number in the range `(0,1)` indicating the (fixed) prior inclusion probability of each coefficient. Or numeric vector of length 2 with positive entries indicating the shape parameters of the Beta distribution. In that case a Beta hyperprior is placed on the prior inclusion probability. `SSVS_p` has only to be specified if `prior="SSVS"`.
`HMP_lambda1`	numeric vector of length 2. Both entries must be positive. The first indicates the shape and the second the rate of the Gamma hyperprior on own-lag coefficients. `HMP_lambda1` has only to be specified if `prior="HMP"`.
`HMP_lambda2`	numeric vector of length 2. Both entries must be positive. The first indicates the shape and the second the rate of the Gamma hyperprior on cross-lag coefficients. `HMP_lambda2` has only to be specified if `prior="HMP"`.
`normal_sds`	numeric vector of length $n$ , where $n = lags M^2$ is the number of all VAR coefficients (excluding the intercept), indicating the prior variances. A single number will be recycled accordingly! Must be positive. `normal_sds` has only to be specified if `prior="normal"`.
`global_grouping`	One of `"global"`, `"equation-wise"`, `"covariate-wise"`, `"olcl-lagwise"` `"fol"` indicating the sub-groups of the semi-global(-local) modifications to HS, R2D2, NG, DL and SSVS prior. Works also with user-specified indicator matrix of dimension `c(lags*M,M)`. Only relevant if `prior="HS"`, `prior="DL"`, `prior="R2D2"`, `prior="NG"` or `prior="SSVS"`.
`...`	Do not use!

Details

For details concerning prior-elicitation for VARs please see Gruber & Kastner (2023).

Currently one can choose between six hierarchical shrinkage priors and a normal prior: prior="HS" stands for the Horseshoe-prior, ⁠prior="R2D2⁠ for the R $^2$ -induced-Dirichlet-decompostion-prior, prior="NG" for the normal-gamma-prior, prior="DL" for the Dirichlet-Laplace-prior, prior="SSVS" for the stochastic-search-variable-selection-prior, prior="HMP" for the semi-hierarchical Minnesota prior and prior=normal for the normal-prior.

Semi-global shrinkage, i.e. group-specific shrinkage for pre-specified subgroups of the coefficients, can be achieved through the argument global_grouping.

Value

A baysianVARs_prior_phi-object.

References

Gruber, L. and Kastner, G. (2023). Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends! arXiv:2206.04902.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Horseshoe prior for a VAR(2)
phi_hs <- specify_prior_phi(data = data, lags = 2L ,prior = "HS")

# Semi-global-local Horseshoe prior for a VAR(2) with semi-global shrinkage parameters for
# cross-lag and own-lag coefficients in each lag
phi_hs_sg <- specify_prior_phi(data = data, lags = 2L, prior = "HS",
global_grouping = "olcl-lagwise")

# Semi-global-local Horseshoe prior for a VAR(2) with equation-wise shrinkage
# construct indicator matrix for equation-wise shrinkage
semi_global_mat <- matrix(1:ncol(data), 2*ncol(data), ncol(data),
byrow = TRUE)
phi_hs_ew <- specify_prior_phi(data = data, lags = 2L, prior = "HS",
global_grouping = semi_global_mat)
# (for equation-wise shrinkage one can also use 'global_grouping = "equation-wise"')


# Estimate model with your prior configuration of choice
mod <- bvar(data, lags = 2L, prior_phi = phi_hs_sg, quiet = TRUE)

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Horseshoe prior for a VAR(2)
phi_hs <- specify_prior_phi(data = data, lags = 2L ,prior = "HS")

# Semi-global-local Horseshoe prior for a VAR(2) with semi-global shrinkage parameters for
# cross-lag and own-lag coefficients in each lag
phi_hs_sg <- specify_prior_phi(data = data, lags = 2L, prior = "HS",
global_grouping = "olcl-lagwise")

# Semi-global-local Horseshoe prior for a VAR(2) with equation-wise shrinkage
# construct indicator matrix for equation-wise shrinkage
semi_global_mat <- matrix(1:ncol(data), 2*ncol(data), ncol(data),
byrow = TRUE)
phi_hs_ew <- specify_prior_phi(data = data, lags = 2L, prior = "HS",
global_grouping = semi_global_mat)
# (for equation-wise shrinkage one can also use 'global_grouping = "equation-wise"')


# Estimate model with your prior configuration of choice
mod <- bvar(data, lags = 2L, prior_phi = phi_hs_sg, quiet = TRUE)

Specify prior on Sigma

Description

Configures prior on the variance-covariance of the VAR.

Usage

specify_prior_sigma(
  data = NULL,
  M = ncol(data),
  type = c("factor", "cholesky"),
  factor_factors = 1L,
  factor_restrict = c("none", "upper"),
  factor_priorfacloadtype = c("rowwiseng", "colwiseng", "normal"),
  factor_priorfacload = 0.1,
  factor_facloadtol = 1e-18,
  factor_priorng = c(1, 1),
  factor_priormu = c(0, 10),
  factor_priorphiidi = c(10, 3),
  factor_priorphifac = c(10, 3),
  factor_priorsigmaidi = 1,
  factor_priorsigmafac = 1,
  factor_priorh0idi = "stationary",
  factor_priorh0fac = "stationary",
  factor_heteroskedastic = TRUE,
  factor_priorhomoskedastic = NA,
  factor_interweaving = 4,
  cholesky_U_prior = c("HS", "DL", "R2D2", "NG", "SSVS", "normal", "HMP"),
  cholesky_U_tol = 1e-18,
  cholesky_heteroscedastic = TRUE,
  cholesky_priormu = c(0, 100),
  cholesky_priorphi = c(20, 1.5),
  cholesky_priorsigma2 = c(0.5, 0.5),
  cholesky_priorh0 = "stationary",
  cholesky_priorhomoscedastic = as.numeric(NA),
  cholesky_DL_a = "1/n",
  cholesky_DL_tol = 0,
  cholesky_R2D2_a = 0.4,
  cholesky_R2D2_b = 0.5,
  cholesky_R2D2_tol = 0,
  cholesky_NG_a = 0.5,
  cholesky_NG_b = 0.5,
  cholesky_NG_c = 0.5,
  cholesky_NG_tol = 0,
  cholesky_SSVS_c0 = 0.001,
  cholesky_SSVS_c1 = 1,
  cholesky_SSVS_p = 0.5,
  cholesky_HMP_lambda3 = c(0.01, 0.01),
  cholesky_normal_sds = 10,
  expert_sv_offset = 0,
  quiet = FALSE,
  ...
)
specify_prior_sigma(
  data = NULL,
  M = ncol(data),
  type = c("factor", "cholesky"),
  factor_factors = 1L,
  factor_restrict = c("none", "upper"),
  factor_priorfacloadtype = c("rowwiseng", "colwiseng", "normal"),
  factor_priorfacload = 0.1,
  factor_facloadtol = 1e-18,
  factor_priorng = c(1, 1),
  factor_priormu = c(0, 10),
  factor_priorphiidi = c(10, 3),
  factor_priorphifac = c(10, 3),
  factor_priorsigmaidi = 1,
  factor_priorsigmafac = 1,
  factor_priorh0idi = "stationary",
  factor_priorh0fac = "stationary",
  factor_heteroskedastic = TRUE,
  factor_priorhomoskedastic = NA,
  factor_interweaving = 4,
  cholesky_U_prior = c("HS", "DL", "R2D2", "NG", "SSVS", "normal", "HMP"),
  cholesky_U_tol = 1e-18,
  cholesky_heteroscedastic = TRUE,
  cholesky_priormu = c(0, 100),
  cholesky_priorphi = c(20, 1.5),
  cholesky_priorsigma2 = c(0.5, 0.5),
  cholesky_priorh0 = "stationary",
  cholesky_priorhomoscedastic = as.numeric(NA),
  cholesky_DL_a = "1/n",
  cholesky_DL_tol = 0,
  cholesky_R2D2_a = 0.4,
  cholesky_R2D2_b = 0.5,
  cholesky_R2D2_tol = 0,
  cholesky_NG_a = 0.5,
  cholesky_NG_b = 0.5,
  cholesky_NG_c = 0.5,
  cholesky_NG_tol = 0,
  cholesky_SSVS_c0 = 0.001,
  cholesky_SSVS_c1 = 1,
  cholesky_SSVS_p = 0.5,
  cholesky_HMP_lambda3 = c(0.01, 0.01),
  cholesky_normal_sds = 10,
  expert_sv_offset = 0,
  quiet = FALSE,
  ...
)

Arguments

`data`	Optional. Data matrix (can be a time series object). Each of $M$ columns is assumed to contain a single time-series of length $T$ .
`M`	positive integer indicating the number of time-series of the VAR.
`type`	character, one of `"factor"` (the default) or `"cholesky"`, indicating which decomposition to be applied to the covariance-matrix.
`factor_factors`	Number of latent factors to be estimated. Only required if `type="factor"`.
`factor_restrict`	Either "upper" or "none", indicating whether the factor loadings matrix should be restricted to have zeros above the diagonal ("upper") or whether all elements should be estimated from the data ("none"). Setting `restrict` to "upper" often stabilizes MCMC estimation and can be important for identifying the factor loadings matrix, however, it generally is a strong prior assumption. Setting `restrict` to "none" is usually the preferred option if identification of the factor loadings matrix is of less concern but covariance estimation or prediction is the goal. Only required if `type="factor"`.
`factor_priorfacloadtype`	Can be `"normal"`, `"rowwiseng"`, `"colwiseng"`. Only required if `type="factor"`. `"normal"`: Normal prior. The value of `priorfacload` is interpreted as the standard deviations of the Gaussian prior distributions for the factor loadings. `"rowwiseng"`: Row-wise Normal-Gamma prior. The value of `priorfacload` is interpreted as the shrinkage parameter `a`. `"colwiseng"`: Column-wise Normal-Gamma prior. The value of `priorfacload` is interpreted as the shrinkage parameter `a`. For details please see Kastner (2019).
`factor_priorfacload`	Either a matrix of dimensions `M` times `factor_factors` with positive elements or a single number (which will be recycled accordingly). Only required if `type="factor"`. The meaning of `factor_priorfacload` depends on the setting of `factor_priorfacloadtype` and is explained there.
`factor_facloadtol`	Minimum number that the absolute value of a factor loadings draw can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. Only required if `type="factor"`.
`factor_priorng`	Two-element vector with positive entries indicating the Normal-Gamma prior's hyperhyperparameters `c` and `d` (cf. Kastner (2019)). Only required if `type="factor"`.
`factor_priormu`	Vector of length 2 denoting prior mean and standard deviation for unconditional levels of the idiosyncratic log variance processes. Only required if `type="factor"`.
`factor_priorphiidi`	Vector of length 2, indicating the shape parameters for the Beta prior distributions of the transformed parameters `(phi+1)/2`, where `phi` denotes the persistence of the idiosyncratic log variances. Only required if `type="factor"`.
`factor_priorphifac`	Vector of length 2, indicating the shape parameters for the Beta prior distributions of the transformed parameters `(phi+1)/2`, where `phi` denotes the persistence of the factor log variances. Only required if `type="factor"`.
`factor_priorsigmaidi`	Vector of length `M` containing the prior volatilities of log variances. If `factor_priorsigmaidi` has exactly one element, it will be recycled for all idiosyncratic log variances. Only required if `type="factor"`.
`factor_priorsigmafac`	Vector of length `factor_factors` containing the prior volatilities of log variances. If `factor_priorsigmafac` has exactly one element, it will be recycled for all factor log variances. Only required if `type="factor"`.
`factor_priorh0idi`	Vector of length 1 or `M`, containing information about the Gaussian prior for the initial idiosyncratic log variances. Only required if `type="factor"`. If an element of `factor_priorh0idi` is a nonnegative number, the conditional prior of the corresponding initial log variance h0 is assumed to be Gaussian with mean 0 and standard deviation `factor_priorh0idi` times $sigma$ . If an element of `factor_priorh0idi` is the string 'stationary', the prior of the corresponding initial log volatility is taken to be from the stationary distribution, i.e. h0 is assumed to be Gaussian with mean 0 and variance $sigma^2/(1-phi^2)$ .
`factor_priorh0fac`	Vector of length 1 or `factor_factors`, containing information about the Gaussian prior for the initial factor log variances. Only required if `type="factor"`. If an element of `factor_priorh0fac` is a nonnegative number, the conditional prior of the corresponding initial log variance h0 is assumed to be Gaussian with mean 0 and standard deviation `factor_priorh0fac` times $sigma$ . If an element of `factor_priorh0fac` is the string 'stationary', the prior of the corresponding initial log volatility is taken to be from the stationary distribution, i.e. h0 is assumed to be Gaussian with mean 0 and variance $sigma^2/(1-phi^2)$ .
`factor_heteroskedastic`	Vector of length 1, 2, or `M + factor_factors`, containing logical values indicating whether time-varying (`factor_heteroskedastic = TRUE`) or constant (`factor_heteroskedastic = FALSE`) variance should be estimated. If `factor_heteroskedastic` is of length 2 it will be recycled accordingly, whereby the first element is used for all idiosyncratic variances and the second element is used for all factor variances. Only required if `type="factor"`.
`factor_priorhomoskedastic`	Only used if at least one element of `factor_heteroskedastic` is set to `FALSE`. In that case, `factor_priorhomoskedastic` must be a matrix with positive entries and dimension c(M, 2). Values in column 1 will be interpreted as the shape and values in column 2 will be interpreted as the rate parameter of the corresponding inverse gamma prior distribution of the idiosyncratic variances. Only required if `type="factor"`.
`factor_interweaving`	The following values for interweaving the factor loadings are accepted (Only required if `type="factor"`): 0: No interweaving. 1: Shallow interweaving through the diagonal entries. 2: Deep interweaving through the diagonal entries. 3: Shallow interweaving through the largest absolute entries in each column. 4: Deep interweaving through the largest absolute entries in each column. For details please see Kastner et al. (2017). A value of 4 is the highly recommended default.
`cholesky_U_prior`	character, one of `"HS"`, `"R2D2"`, `"NG"`, `"DL"`, `"SSVS"`, `"HMP"` or `"normal"`. Only required if `type="cholesky"`.
`cholesky_U_tol`	Minimum number that the absolute value of an free off-diagonal element of an $U$ -draw can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. Only required if `type="cholesky"`.
`cholesky_heteroscedastic`	single logical indicating whether time-varying (`cholesky_heteroscedastic = TRUE`) or constant (`cholesky_heteroscedastic = FALSE`) variance should be estimated. Only required if `type="cholesky"`.
`cholesky_priormu`	Vector of length 2 denoting prior mean and standard deviation for unconditional levels of the log variance processes. Only required if `type="cholesky"`.
`cholesky_priorphi`	Vector of length 2, indicating the shape parameters for the Beta prior distributions of the transformed parameters `(phi+1)/2`, where `phi` denotes the persistence of the log variances. Only required if `type="cholesky"`.
`cholesky_priorsigma2`	Vector of length 2, indicating the shape and the rate for the Gamma prior distributions on the variance of the log variance processes. (Currently only one global setting for all $M$ processes is supported). Only required if `type="cholesky"`.
`cholesky_priorh0`	Vector of length 1 or `M`, containing information about the Gaussian prior for the initial idiosyncratic log variances. Only required if `type="cholesky"`. If an element of `cholesky_priorh0` is a nonnegative number, the conditional prior of the corresponding initial log variance h0 is assumed to be Gaussian with mean 0 and standard deviation `cholesky_priorh0` times $sigma$ . If an element of `cholesky_priorh0` is the string 'stationary', the prior of the corresponding initial log volatility is taken to be from the stationary distribution, i.e. h0 is assumed to be Gaussian with mean 0 and variance $sigma^2/(1-phi^2)$ .
`cholesky_priorhomoscedastic`	Only used if `cholesky_heteroscedastic=FALSE`. In that case, `cholesky_priorhomoscedastic` must be a matrix with positive entries and dimension c(M, 2). Values in column 1 will be interpreted as the shape and values in column 2 will be interpreted as the scale parameter of the corresponding inverse gamma prior distribution of the variances. Only required if `type="cholesky"`.
`cholesky_DL_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains s support points and the second column contains the associated prior probabilities. `cholesky_DL_a` has only to be specified if `cholesky_U_prior="DL"`.
`cholesky_DL_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the Dirichlet Laplace prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `DL_tol` has only to be specified if `cholesky_U_prior="DL"`.
`cholesky_R2D2_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains s support points and the second column contains the associated prior probabilities. cholesky_R2D2_a has only to be specified if `cholesky_U_prior="R2D2"`.
`cholesky_R2D2_b`	single positive number, where greater values indicate heavier regularization. `cholesky_R2D2_b` has only to be specified if `cholesky_U_prior="R2D2"`.
`cholesky_R2D2_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the R2D2 prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `cholesky_R2D2_tol` has only to be specified if `cholesky_U_prior="R2D2"`.
`cholesky_NG_a`	(Single) positive real number. The value is interpreted as the concentration parameter for the local scales. Smaller values enforce heavier shrinkage. A matrix of dimension `c(s,2)` specifies a discrete hyperprior, where the first column contains s support points and the second column contains the associated prior probabilities. `cholesky_NG_a` has only to be specified if `cholesky_U_prior="NG"`.
`cholesky_NG_b`	(Single) positive real number. The value indicates the shape parameter of the inverse gamma prior on the global scales. `cholesky_NG_b` has only to be specified if `cholesky_U_prior="NG"`.
`cholesky_NG_c`	(Single) positive real number. The value indicates the scale parameter of the inverse gamma prior on the global scales. Expert option would be to set the scale parameter proportional to NG_a. E.g. in the case where a discrete hyperprior for NG_a is chosen, a desired proportion of let's say 0.2 is achieved by setting NG_c="0.2a" (character input!). `cholesky_NG_c` has only to be specified if `cholesky_U_prior="NG"`.
`cholesky_NG_tol`	Minimum number that a parameter draw of one of the shrinking parameters of the normal-gamma prior can take. Prevents numerical issues that can appear when strong shrinkage is enforced if chosen to be greater than zero. `cholesky_NG_tol` has only to be specified if `cholesky_U_prior="NG"`.
`cholesky_SSVS_c0`	single positive number indicating the (unscaled) standard deviation of the spike component. `cholesky_SSVS_c0` has only to be specified if `choleksy_U_prior="SSVS"`. It should be that $SSVS_{c0} \ll SSVS_{c1}$ !
`cholesky_SSVS_c1`	single positive number indicating the (unscaled) standard deviation of the slab component. `cholesky_SSVS_c1` has only to be specified if `choleksy_U_prior="SSVS"`. It should be that $SSVS_{c0} \ll SSVS_{c1}$ !
`cholesky_SSVS_p`	Either a single positive number in the range `⁠(0,1)⁠` indicating the (fixed) prior inclusion probability of each coefficient. Or numeric vector of length 2 with positive entries indicating the shape parameters of the Beta distribution. In that case a Beta hyperprior is placed on the prior inclusion probability. `cholesky_SSVS_p` has only to be specified if `choleksy_U_prior="SSVS"`.
`cholesky_HMP_lambda3`	numeric vector of length 2. Both entries must be positive. The first indicates the shape and the second the rate of the Gamma hyperprior on the contemporaneous coefficients. `cholesky_HMP_lambda3` has only to be specified if `choleksy_U_prior="HMP"`.
`cholesky_normal_sds`	numeric vector of length $\frac{M^2-M}{2}$ , indicating the prior variances for the free off-diagonal elements in $U$ . A single number will be recycled accordingly! Must be positive. `cholesky_normal_sds` has only to be specified if `choleksy_U_prior="normal"`.
`expert_sv_offset`	... Do not use!
`quiet`	logical indicating whether informative output should be omitted.
`...`	Do not use!

Details

Value

Object of class bayesianVARs_prior_sigma.

References

Kastner, G. (2019). Sparse Bayesian Time-Varying Covariance Estimation in Many Dimensions Journal of Econometrics, 210(1), 98–115, doi:10.1016/j.jeconom.2018.11.007

Kastner, G., Frühwirth-Schnatter, S., and Lopes, H.F. (2017). Efficient Bayesian Inference for Multivariate Factor Stochastic Volatility Models. Journal of Computational and Graphical Statistics, 26(4), 905–917, doi:10.1080/10618600.2017.1322091.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# examples with stochastic volatility (heteroscedasticity) -----------------
# factor-decomposition with 2 factors and colwise normal-gamma prior on the loadings
sigma_factor_cng_sv <- specify_prior_sigma(data = data, type = "factor",
factor_factors = 2L, factor_priorfacloadtype = "colwiseng", factor_heteroskedastic = TRUE)

# cholesky-decomposition with Dirichlet-Laplace prior on U
sigma_cholesky_dl_sv <- specify_prior_sigma(data = data, type = "cholesky",
cholesky_U_prior = "DL", cholesky_DL_a = 0.5, cholesky_heteroscedastic = TRUE)

# examples without stochastic volatility (homoscedasticity) ----------------
# factor-decomposition with 2 factors and colwise normal-gamma prior on the loadings
sigma_factor_cng <- specify_prior_sigma(data = data, type = "factor",
factor_factors = 2L, factor_priorfacloadtype = "colwiseng",
factor_heteroskedastic = FALSE, factor_priorhomoskedastic = matrix(c(0.5,0.5),
ncol(data), 2))

# cholesky-decomposition with Horseshoe prior on U
sigma_cholesky_dl <- specify_prior_sigma(data = data, type = "cholesky",
cholesky_U_prior = "HS", cholesky_heteroscedastic = FALSE)


# Estimate model with your prior configuration of choice
mod <- bvar(data, prior_sigma = sigma_factor_cng_sv, quiet = TRUE)

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# examples with stochastic volatility (heteroscedasticity) -----------------
# factor-decomposition with 2 factors and colwise normal-gamma prior on the loadings
sigma_factor_cng_sv <- specify_prior_sigma(data = data, type = "factor",
factor_factors = 2L, factor_priorfacloadtype = "colwiseng", factor_heteroskedastic = TRUE)

# cholesky-decomposition with Dirichlet-Laplace prior on U
sigma_cholesky_dl_sv <- specify_prior_sigma(data = data, type = "cholesky",
cholesky_U_prior = "DL", cholesky_DL_a = 0.5, cholesky_heteroscedastic = TRUE)

# examples without stochastic volatility (homoscedasticity) ----------------
# factor-decomposition with 2 factors and colwise normal-gamma prior on the loadings
sigma_factor_cng <- specify_prior_sigma(data = data, type = "factor",
factor_factors = 2L, factor_priorfacloadtype = "colwiseng",
factor_heteroskedastic = FALSE, factor_priorhomoskedastic = matrix(c(0.5,0.5),
ncol(data), 2))

# cholesky-decomposition with Horseshoe prior on U
sigma_cholesky_dl <- specify_prior_sigma(data = data, type = "cholesky",
cholesky_U_prior = "HS", cholesky_heteroscedastic = FALSE)


# Estimate model with your prior configuration of choice
mod <- bvar(data, prior_sigma = sigma_factor_cng_sv, quiet = TRUE)

Stable posterior draws

Description

stable_bvar() detects and discards all posterior draws of an bayesianVARs_bvar object that do not fulfill the stability condition: A VAR(p) model is considered as stable only if the eigenvalues of the companion form matrix lie inside the unit circle.

Usage

stable_bvar(object, quiet = FALSE)
stable_bvar(object, quiet = FALSE)

Arguments

`object`	A `bayesianVARs_bvar` object obtained via `bvar()`.
`quiet`	logical indicating whether informative output should be omitted.

Value

An object of type bayesianVARs_bvar.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Discard "unstable" draws
stable_mod <- stable_bvar(mod)

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Discard "unstable" draws
stable_mod <- stable_bvar(mod)

Summary method for bayesianVARs_bvar objects

Description

Summary method for bayesianVARs_bvar objects.

Usage

## S3 method for class 'bayesianVARs_bvar'
summary(object, quantiles = c(0.025, 0.25, 0.5, 0.75, 0.975), ...)
## S3 method for class 'bayesianVARs_bvar'
summary(object, quantiles = c(0.025, 0.25, 0.5, 0.75, 0.975), ...)

Arguments

`object`	A `bayesianVARs_bvar` object obtained via `bvar()`.
`quantiles`	numeric vector which quantiles to compute.
`...`	Currently ignored!

Value

An object of type summary.bayesianVARs_bvar.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate model
mod <- bvar(data, quiet = TRUE)

# Summary
sum <- summary(mod)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Estimate model
mod <- bvar(data, quiet = TRUE)

# Summary
sum <- summary(mod)

Summary statistics for bayesianVARs posterior draws.

Description

Summary statistics for bayesianVARs posterior draws.

Usage

## S3 method for class 'bayesianVARs_draws'
summary(object, quantiles = c(0.25, 0.5, 0.75), ...)
## S3 method for class 'bayesianVARs_draws'
summary(object, quantiles = c(0.25, 0.5, 0.75), ...)

Arguments

`object`	An object of class `bayesianVARs_draws` usually obtained through extractors like `coef.bayesianVARs_bvar()` and `vcov.bayesianVARs_bvar()`.
`quantiles`	A vector of quantiles to evaluate.
`...`	Currently ignored.

Value

A list object of class bayesianVARs_draws_summary holding

mean: Vector or matrix containing the posterior mean.
sd: Vector or matrix containing the posterior standard deviation .
quantiles: Array containing the posterior quantiles.

Examples


# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]
# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of VAR coefficients
bvar_coefs <- coef(mod)

# Compute summary statistics
summary_stats <- summary(bvar_coefs)

# Compute summary statistics of VAR coefficients without using coef()
summary_stats <- summary(mod$PHI)

# Test which list elements of 'mod' are of class 'bayesianVARs_draws'.
names(mod)[sapply(names(mod), function(x) inherits(mod[[x]], "bayesianVARs_draws"))]

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]
# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of VAR coefficients
bvar_coefs <- coef(mod)

# Compute summary statistics
summary_stats <- summary(bvar_coefs)

# Compute summary statistics of VAR coefficients without using coef()
summary_stats <- summary(mod$PHI)

# Test which list elements of 'mod' are of class 'bayesianVARs_draws'.
names(mod)[sapply(names(mod), function(x) inherits(mod[[x]], "bayesianVARs_draws"))]

Summary method for bayesianVARs_predict objects

Description

Summary method for bayesianVARs_predict objects.

Usage

## S3 method for class 'bayesianVARs_predict'
summary(object, ...)
## S3 method for class 'bayesianVARs_predict'
summary(object, ...)

Arguments

`object`	A `bayesianVARs_predict` object obtained via `predict.bayesianVARs_bvar()`.
`...`	Currently ignored!

Value

A summary.bayesianVARs_predict object.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step ahead posterior predictive
predictions <- predict(mod, ahead = 1L)
summary(predictions)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]

# Split data in train and test
train <- data[1:(nrow(data)-4),]
test <- data[-c(1:(nrow(data)-4)),]

# Estimate model using train data only
mod <- bvar(train, quiet = TRUE)

# Simulate from 1-step ahead posterior predictive
predictions <- predict(mod, ahead = 1L)
summary(predictions)

Data from the US-economy

Description

21 selected quarterly time-series from 1953:Q1 to 2021:Q2. From FRED-QD data base (McCracken and Ng, 2021). Release date 2021-07. Data is transformed to be interpreted as growth-rates (first log-differences with the exception of interest rates, which are already growth rates).

Usage

usmacro_growth
usmacro_growth

Format

A matrix with 247 rows and 21 columns.

Source

Raw (untransformed) data available at https://www.stlouisfed.org/research/economists/mccracken/fred-databases, https://files.stlouisfed.org/files/htdocs/fred-md/quarterly/2021-07.csv.

References

McCracken, M. W. and Ng, S. (2021). FRED-QD: A Quarterly Database for Macroeconomic Research, Review, Federal Reserve Bank of St. Louis, 103(1), 1–44, doi:10.20955/r.103.1-44.

Extract posterior draws of the (time-varying) variance-covariance matrix for a VAR model

Description

Returns the posterior draws of the possibly time-varying variance-covariance matrix of a VAR estimated via bvar(). Returns the full paths if sv_keep="all" when calling bvar(). Otherwise, the draws of the variance-covariance matrix for the last observation are returned, only.

Usage

## S3 method for class 'bayesianVARs_bvar'
vcov(object, t = seq_len(nrow(object$logvar)), ...)
## S3 method for class 'bayesianVARs_bvar'
vcov(object, t = seq_len(nrow(object$logvar)), ...)

Arguments

`object`	An object of class `bayesianVARs_bvar` obtained via `bvar()`.
`t`	Vector indicating which points in time should be extracted, defaults to all.
`...`	Currently ignored.

Value

An array of class bayesianVARs_draws of dimension $T \times M \times M \times draws$ , where $T$ is the number of observations, $M$ the number of time-series and $draws$ the number of stored posterior draws.

Examples

# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]
# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of the variance-covariance matrix
bvar_vcov <- vcov(mod)
# Access a subset of the usmacro_growth dataset
data <- usmacro_growth[,c("GDPC1", "CPIAUCSL", "FEDFUNDS")]
# Estimate a model
mod <- bvar(data, sv_keep = "all", quiet = TRUE)

# Extract posterior draws of the variance-covariance matrix
bvar_vcov <- vcov(mod)

Package 'bayesianVARs'

Help Index

Extract or Replace Parts of a bayesianVARs_coef object

Description

Usage

Arguments

Value

Examples

Extract or Replace Parts of a bayesianVARs_draws object

Description

Usage

Arguments

Value

Examples

Markov Chain Monte Carlo Sampling for Bayesian Vectorautoregressions

Description

Usage

Arguments

Details

Value

MCMC algorithm

References

See Also

Examples

Extract VAR coefficients

Description

Usage

Arguments

Value

See Also

Examples

Simulate fitted/predicted historical values for an estimated VAR model

Description

Usage

Arguments

Value

Examples

Draw from generalized inverse Gaussian

Description

Usage

Arguments

Value

Examples

Pairwise visualization of out-of-sample posterior predictive densities.

Description

Usage

Arguments

Value

Note

See Also

Examples

Plot method for bayesianVARs_bvar

Description

Usage

Arguments

Value

See Also

Examples

Visualization of in-sample fit of an estimated VAR.

Description

Usage

Arguments

Value

See Also

Examples

Fan chart

Description

Usage

Arguments

Value

See Also

Examples

Posterior heatmaps for VAR coefficients or variance-covariance matrices

Description

Usage

Arguments

Value

See Also

Examples

Predict method for Bayesian VARs