# Bayesian Vector Heterogeneous Autoregressive Modeling

## Documentation for package ‘bvhar’ version 2.1.2

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

A B C D E F G H I K L M P R S V

## -- A --

AIC.bvarflat | Fitting Bayesian VAR(p) of Flat Prior
AIC.bvarmn | Fitting Bayesian VAR(p) of Minnesota Prior
AIC.bvharmn | Fitting Bayesian VHAR of Minnesota Prior
AIC.varlse | Fitting Vector Autoregressive Model of Order p Model
AIC.vharlse | Fitting Vector Heterogeneous Autoregressive Model
autolayer.predbvhar | Plot Forecast Result
autoplot.bvhardynsp | Dynamic Spillover Indices Plot
autoplot.bvharirf | Plot Impulse Responses
autoplot.bvharsp | Plot the Result of BVAR and BVHAR MCMC
autoplot.normaliw | Residual Plot for Minnesota Prior VAR Model
autoplot.predbvhar | Plot Forecast Result
autoplot.summary.bvharsp | Plot the Heatmap of SSVS Coefficients
autoplot.summary.normaliw | Density Plot for Minnesota Prior VAR Model

## -- B --

BIC.bvarflat | Fitting Bayesian VAR(p) of Flat Prior
BIC.bvarmn | Fitting Bayesian VAR(p) of Minnesota Prior
BIC.bvharmn | Fitting Bayesian VHAR of Minnesota Prior
BIC.varlse | Fitting Vector Autoregressive Model of Order p Model
BIC.vharlse | Fitting Vector Heterogeneous Autoregressive Model
bound_bvhar | Setting Empirical Bayes Optimization Bounds
bvar_flat | Fitting Bayesian VAR(p) of Flat Prior
bvar_horseshoe | Fitting Bayesian VAR(p) of Horseshoe Prior
bvar_minnesota | Fitting Bayesian VAR(p) of Minnesota Prior
bvar_ssvs | Fitting Bayesian VAR(p) of SSVS Prior
bvar_sv | Fitting Bayesian VAR-SV
bvhar_horseshoe | Fitting Bayesian VHAR of Horseshoe Prior
bvhar_minnesota | Fitting Bayesian VHAR of Minnesota Prior
bvhar_ssvs | Fitting Bayesian VHAR of SSVS Prior
bvhar_sv | Fitting Bayesian VHAR-SV

## -- C --

choose_bayes | Finding the Set of Hyperparameters of Bayesian Model
choose_bvar | Finding the Set of Hyperparameters of Individual Bayesian Model
choose_bvhar | Finding the Set of Hyperparameters of Individual Bayesian Model
choose_ssvs | Choose the Hyperparameters Set of SSVS-VAR using a Default Semiautomatic Approach
choose_var | Choose the Best VAR based on Information Criteria
coef | Coefficient Matrix of Multivariate Time Series Models
coef.bvarflat | Coefficient Matrix of Multivariate Time Series Models
coef.bvarmn | Coefficient Matrix of Multivariate Time Series Models
coef.bvharmn | Coefficient Matrix of Multivariate Time Series Models
coef.bvharsp | Coefficient Matrix of Multivariate Time Series Models
coef.summary.bvharsp | Coefficient Matrix of Multivariate Time Series Models
coef.varlse | Coefficient Matrix of Multivariate Time Series Models
coef.vharlse | Coefficient Matrix of Multivariate Time Series Models
compute_dic | Deviance Information Criterion of Multivariate Time Series Model
compute_dic.bvarmn | Deviance Information Criterion of Multivariate Time Series Model
compute_logml | Extracting Log of Marginal Likelihood
compute_logml.bvarmn | Extracting Log of Marginal Likelihood
compute_logml.bvharmn | Extracting Log of Marginal Likelihood
confusion | Evaluate the Sparsity Estimation Based on Confusion Matrix
confusion.summary.bvharsp | Evaluate the Sparsity Estimation Based on Confusion Matrix
conf_fdr | Evaluate the Sparsity Estimation Based on FDR
conf_fdr.summary.bvharsp | Evaluate the Sparsity Estimation Based on FDR
conf_fnr | Evaluate the Sparsity Estimation Based on FNR
conf_fnr.summary.bvharsp | Evaluate the Sparsity Estimation Based on FNR
conf_fscore | Evaluate the Sparsity Estimation Based on F1 Score
conf_fscore.summary.bvharsp | Evaluate the Sparsity Estimation Based on F1 Score
conf_prec | Evaluate the Sparsity Estimation Based on Precision
conf_prec.summary.bvharsp | Evaluate the Sparsity Estimation Based on Precision
conf_recall | Evaluate the Sparsity Estimation Based on Recall
conf_recall.summary.bvharsp | Evaluate the Sparsity Estimation Based on Recall

## -- D --

divide_ts | Split a Time Series Dataset into Train-Test Set
dynamic_spillover | Dynamic Spillover
dynamic_spillover.ldltmod | Dynamic Spillover
dynamic_spillover.normaliw | Dynamic Spillover
dynamic_spillover.olsmod | Dynamic Spillover
dynamic_spillover.svmod | Dynamic Spillover

## -- E --

etf_vix | CBOE ETF Volatility Index Dataset

## -- F --

fitted | Fitted Matrix from Multivariate Time Series Models
fitted.bvarflat | Fitted Matrix from Multivariate Time Series Models
fitted.bvarmn | Fitted Matrix from Multivariate Time Series Models
fitted.bvharmn | Fitted Matrix from Multivariate Time Series Models
fitted.varlse | Fitted Matrix from Multivariate Time Series Models
fitted.vharlse | Fitted Matrix from Multivariate Time Series Models
forecast_expand | Out-of-sample Forecasting based on Expanding Window
forecast_expand.ldltmod | Out-of-sample Forecasting based on Expanding Window
forecast_expand.normaliw | Out-of-sample Forecasting based on Expanding Window
forecast_expand.olsmod | Out-of-sample Forecasting based on Expanding Window
forecast_expand.svmod | Out-of-sample Forecasting based on Expanding Window
forecast_roll | Out-of-sample Forecasting based on Rolling Window
forecast_roll.ldltmod | Out-of-sample Forecasting based on Rolling Window
forecast_roll.normaliw | Out-of-sample Forecasting based on Rolling Window
forecast_roll.olsmod | Out-of-sample Forecasting based on Rolling Window
forecast_roll.svmod | Out-of-sample Forecasting based on Rolling Window
FPE | Final Prediction Error Criterion
FPE.varlse | Final Prediction Error Criterion
FPE.vharlse | Final Prediction Error Criterion
fromse | Evaluate the Estimation Based on Frobenius Norm
fromse.bvharsp | Evaluate the Estimation Based on Frobenius Norm

## -- G --

geom_eval | Adding Test Data Layer
gg_loss | Compare Lists of Models

## -- H --

HQ | Hannan-Quinn Criterion
HQ.bvarflat | Hannan-Quinn Criterion
HQ.bvarmn | Hannan-Quinn Criterion
HQ.bvharmn | Hannan-Quinn Criterion
HQ.logLik | Hannan-Quinn Criterion
HQ.varlse | Hannan-Quinn Criterion
HQ.vharlse | Hannan-Quinn Criterion

## -- I --

init_ssvs | Initial Parameters of Stochastic Search Variable Selection (SSVS) Model
irf | Impulse Response Analysis
irf.varlse | Impulse Response Analysis
irf.vharlse | Impulse Response Analysis
is.boundbvharemp | Setting Empirical Bayes Optimization Bounds
is.bvarflat | Fitting Bayesian VAR(p) of Flat Prior
is.bvarmn | Fitting Bayesian VAR(p) of Minnesota Prior
is.bvharcv | Out-of-sample Forecasting based on Rolling Window
is.bvharemp | Finding the Set of Hyperparameters of Individual Bayesian Model
is.bvharirf | Impulse Response Analysis
is.bvharmn | Fitting Bayesian VHAR of Minnesota Prior
is.bvharmod | Fitting Vector Autoregressive Model of Order p Model
is.bvharpriorspec | Hyperpriors for Bayesian Models
is.bvharspec | Hyperparameters for Bayesian Models
is.covspec | Covariance Matrix Prior Specification
is.dlspec | Dirichlet-Laplace Hyperparameter for Coefficients and Contemporaneous Coefficients
is.horseshoespec | Horseshoe Prior Specification
is.interceptspec | Prior for Constant Term
is.ldltspec | Covariance Matrix Prior Specification
is.ngspec | Normal-Gamma Hyperparameter for Coefficients and Contemporaneous Coefficients
is.predbvhar | Forecasting Multivariate Time Series
is.ssvsinit | Initial Parameters of Stochastic Search Variable Selection (SSVS) Model
is.ssvsinput | Stochastic Search Variable Selection (SSVS) Hyperparameter for Coefficients Matrix and Cholesky Factor
is.stable | Stability of the process
is.stable.bvarflat | Stability of the process
is.stable.bvarmn | Stability of the process
is.stable.bvharmn | Stability of the process
is.stable.varlse | Stability of the process
is.stable.vharlse | Stability of the process
is.svspec | Covariance Matrix Prior Specification
is.varlse | Fitting Vector Autoregressive Model of Order p Model
is.vharlse | Fitting Vector Heterogeneous Autoregressive Model

## -- K --

knit_print.boundbvharemp | Setting Empirical Bayes Optimization Bounds
knit_print.bvarflat | Fitting Bayesian VAR(p) of Flat Prior
knit_print.bvarhm | Fitting Bayesian VAR(p) of Minnesota Prior
knit_print.bvarhs | Fitting Bayesian VAR(p) of Horseshoe Prior
knit_print.bvarldlt | Fitting Bayesian VAR with Coefficient and Covariance Prior
knit_print.bvarmn | Fitting Bayesian VAR(p) of Minnesota Prior
knit_print.bvarssvs | Fitting Bayesian VAR(p) of SSVS Prior
knit_print.bvarsv | Fitting Bayesian VAR-SV
knit_print.bvharcv | Out-of-sample Forecasting based on Rolling Window
knit_print.bvhardynsp | Dynamic Spillover
knit_print.bvharemp | Finding the Set of Hyperparameters of Individual Bayesian Model
knit_print.bvharhm | Fitting Bayesian VHAR of Minnesota Prior
knit_print.bvharhs | Fitting Bayesian VHAR of Horseshoe Prior
knit_print.bvharirf | Impulse Response Analysis
knit_print.bvharldlt | Fitting Bayesian VHAR with Coefficient and Covariance Prior
knit_print.bvharmn | Fitting Bayesian VHAR of Minnesota Prior
knit_print.bvharpriorspec | Hyperpriors for Bayesian Models
knit_print.bvharspec | Hyperparameters for Bayesian Models
knit_print.bvharspillover | h-step ahead Normalized Spillover
knit_print.bvharssvs | Fitting Bayesian VHAR of SSVS Prior
knit_print.bvharsv | Fitting Bayesian VHAR-SV
knit_print.horseshoespec | Horseshoe Prior Specification
knit_print.interceptspec | Prior for Constant Term
knit_print.predbvhar | Forecasting Multivariate Time Series
knit_print.ssvsinit | Initial Parameters of Stochastic Search Variable Selection (SSVS) Model
knit_print.ssvsinput | Stochastic Search Variable Selection (SSVS) Hyperparameter for Coefficients Matrix and Cholesky Factor
knit_print.summary.bvharsp | Summarizing BVAR and BVHAR with Shrinkage Priors
knit_print.summary.normaliw | Summarizing Bayesian Multivariate Time Series Model
knit_print.summary.varlse | Summarizing Vector Autoregressive Model
knit_print.summary.vharlse | Summarizing Vector HAR Model
knit_print.varlse | Fitting Vector Autoregressive Model of Order p Model
knit_print.vharlse | Fitting Vector Heterogeneous Autoregressive Model

## -- L --

logLik.bvarflat | Fitting Bayesian VAR(p) of Flat Prior
logLik.bvarmn | Fitting Bayesian VAR(p) of Minnesota Prior
logLik.bvharmn | Fitting Bayesian VHAR of Minnesota Prior
logLik.varlse | Fitting Vector Autoregressive Model of Order p Model
logLik.vharlse | Fitting Vector Heterogeneous Autoregressive Model

## -- M --

mae | Evaluate the Model Based on MAE (Mean Absolute Error)
mae.bvharcv | Evaluate the Model Based on MAE (Mean Absolute Error)
mae.predbvhar | Evaluate the Model Based on MAE (Mean Absolute Error)
mape | Evaluate the Model Based on MAPE (Mean Absolute Percentage Error)
mape.bvharcv | Evaluate the Model Based on MAPE (Mean Absolute Percentage Error)
mape.predbvhar | Evaluate the Model Based on MAPE (Mean Absolute Percentage Error)
mase | Evaluate the Model Based on MASE (Mean Absolute Scaled Error)
mase.bvharcv | Evaluate the Model Based on MASE (Mean Absolute Scaled Error)
mase.predbvhar | Evaluate the Model Based on MASE (Mean Absolute Scaled Error)
mrae | Evaluate the Model Based on MRAE (Mean Relative Absolute Error)
mrae.bvharcv | Evaluate the Model Based on MRAE (Mean Relative Absolute Error)
mrae.predbvhar | Evaluate the Model Based on MRAE (Mean Relative Absolute Error)
mse | Evaluate the Model Based on MSE (Mean Square Error)
mse.bvharcv | Evaluate the Model Based on MSE (Mean Square Error)
mse.predbvhar | Evaluate the Model Based on MSE (Mean Square Error)

## -- P --

predict | Forecasting Multivariate Time Series
predict.bvarflat | Forecasting Multivariate Time Series
predict.bvarhs | Forecasting Multivariate Time Series
predict.bvarldlt | Forecasting Multivariate Time Series
predict.bvarmn | Forecasting Multivariate Time Series
predict.bvarssvs | Forecasting Multivariate Time Series
predict.bvarsv | Forecasting Multivariate Time Series
predict.bvharhs | Forecasting Multivariate Time Series
predict.bvharldlt | Forecasting Multivariate Time Series
predict.bvharmn | Forecasting Multivariate Time Series
predict.bvharssvs | Forecasting Multivariate Time Series
predict.bvharsv | Forecasting Multivariate Time Series
predict.varlse | Forecasting Multivariate Time Series
predict.vharlse | Forecasting Multivariate Time Series
print.boundbvharemp | Setting Empirical Bayes Optimization Bounds
print.bvarflat | Fitting Bayesian VAR(p) of Flat Prior
print.bvarhm | Fitting Bayesian VAR(p) of Minnesota Prior
print.bvarhs | Fitting Bayesian VAR(p) of Horseshoe Prior
print.bvarldlt | Fitting Bayesian VAR with Coefficient and Covariance Prior
print.bvarmn | Fitting Bayesian VAR(p) of Minnesota Prior
print.bvarssvs | Fitting Bayesian VAR(p) of SSVS Prior
print.bvarsv | Fitting Bayesian VAR-SV
print.bvharcv | Out-of-sample Forecasting based on Rolling Window
print.bvhardynsp | Dynamic Spillover
print.bvharemp | Finding the Set of Hyperparameters of Individual Bayesian Model
print.bvharhm | Fitting Bayesian VHAR of Minnesota Prior
print.bvharhs | Fitting Bayesian VHAR of Horseshoe Prior
print.bvharirf | Impulse Response Analysis
print.bvharldlt | Fitting Bayesian VHAR with Coefficient and Covariance Prior
print.bvharmn | Fitting Bayesian VHAR of Minnesota Prior
print.bvharpriorspec | Hyperpriors for Bayesian Models
print.bvharspec | Hyperparameters for Bayesian Models
print.bvharspillover | h-step ahead Normalized Spillover
print.bvharssvs | Fitting Bayesian VHAR of SSVS Prior
print.bvharsv | Fitting Bayesian VHAR-SV
print.covspec | Covariance Matrix Prior Specification
print.dlspec | Dirichlet-Laplace Hyperparameter for Coefficients and Contemporaneous Coefficients
print.horseshoespec | Horseshoe Prior Specification
print.interceptspec | Prior for Constant Term
print.ngspec | Normal-Gamma Hyperparameter for Coefficients and Contemporaneous Coefficients
print.predbvhar | Forecasting Multivariate Time Series
print.ssvsinit | Initial Parameters of Stochastic Search Variable Selection (SSVS) Model
print.ssvsinput | Stochastic Search Variable Selection (SSVS) Hyperparameter for Coefficients Matrix and Cholesky Factor
print.summary.bvharsp | Summarizing BVAR and BVHAR with Shrinkage Priors
print.summary.normaliw | Summarizing Bayesian Multivariate Time Series Model
print.summary.varlse | Summarizing Vector Autoregressive Model
print.summary.vharlse | Summarizing Vector HAR Model
print.varlse | Fitting Vector Autoregressive Model of Order p Model
print.vharlse | Fitting Vector Heterogeneous Autoregressive Model

## -- R --

relmae | Evaluate the Model Based on RelMAE (Relative MAE)
relmae.bvharcv | Evaluate the Model Based on RelMAE (Relative MAE)
relmae.predbvhar | Evaluate the Model Based on RelMAE (Relative MAE)
relspne | Evaluate the Estimation Based on Relative Spectral Norm Error
relspne.bvharsp | Evaluate the Estimation Based on Relative Spectral Norm Error
residuals | Residual Matrix from Multivariate Time Series Models
residuals.bvarflat | Residual Matrix from Multivariate Time Series Models
residuals.bvarmn | Residual Matrix from Multivariate Time Series Models
residuals.bvharmn | Residual Matrix from Multivariate Time Series Models
residuals.varlse | Residual Matrix from Multivariate Time Series Models
residuals.vharlse | Residual Matrix from Multivariate Time Series Models
rmafe | Evaluate the Model Based on RMAFE
rmafe.bvharcv | Evaluate the Model Based on RMAFE
rmafe.predbvhar | Evaluate the Model Based on RMAFE
rmape | Evaluate the Model Based on RMAPE (Relative MAPE)
rmape.bvharcv | Evaluate the Model Based on RMAPE (Relative MAPE)
rmape.predbvhar | Evaluate the Model Based on RMAPE (Relative MAPE)
rmase | Evaluate the Model Based on RMASE (Relative MASE)
rmase.bvharcv | Evaluate the Model Based on RMASE (Relative MASE)
rmase.predbvhar | Evaluate the Model Based on RMASE (Relative MASE)
rmsfe | Evaluate the Model Based on RMSFE
rmsfe.bvharcv | Evaluate the Model Based on RMSFE
rmsfe.predbvhar | Evaluate the Model Based on RMSFE

## -- S --

set_bvar | Hyperparameters for Bayesian Models
set_bvar_flat | Hyperparameters for Bayesian Models
set_bvhar | Hyperparameters for Bayesian Models
set_dl | Dirichlet-Laplace Hyperparameter for Coefficients and Contemporaneous Coefficients
set_horseshoe | Horseshoe Prior Specification
set_intercept | Prior for Constant Term
set_lambda | Hyperpriors for Bayesian Models
set_ldlt | Covariance Matrix Prior Specification
set_ng | Normal-Gamma Hyperparameter for Coefficients and Contemporaneous Coefficients
set_psi | Hyperpriors for Bayesian Models
set_ssvs | Stochastic Search Variable Selection (SSVS) Hyperparameter for Coefficients Matrix and Cholesky Factor
set_sv | Covariance Matrix Prior Specification
set_weight_bvhar | Hyperparameters for Bayesian Models
sim_gig | Generate Generalized Inverse Gaussian Distribution
sim_horseshoe_var | Generate Horseshoe Parameters
sim_horseshoe_vhar | Generate Horseshoe Parameters
sim_iw | Generate Inverse-Wishart Random Matrix
sim_matgaussian | Generate Matrix Normal Random Matrix
sim_mncoef | Generate Minnesota BVAR Parameters
sim_mniw | Generate Normal-IW Random Family
sim_mnormal | Generate Multivariate Normal Random Vector
sim_mnvhar_coef | Generate Minnesota BVAR Parameters
sim_mvt | Generate Multivariate t Random Vector
sim_ssvs_var | Generate SSVS Parameters
sim_ssvs_vhar | Generate SSVS Parameters
sim_var | Generate Multivariate Time Series Process Following VAR(p)
sim_vhar | Generate Multivariate Time Series Process Following VAR(p)
spillover | h-step ahead Normalized Spillover
spillover.bvarldlt | h-step ahead Normalized Spillover
spillover.bvharldlt | h-step ahead Normalized Spillover
spillover.normaliw | h-step ahead Normalized Spillover
spillover.olsmod | h-step ahead Normalized Spillover
spne | Evaluate the Estimation Based on Spectral Norm Error
spne.bvharsp | Evaluate the Estimation Based on Spectral Norm Error
stableroot | Roots of characteristic polynomial
stableroot.bvarflat | Roots of characteristic polynomial
stableroot.bvarmn | Roots of characteristic polynomial
stableroot.bvharmn | Roots of characteristic polynomial
stableroot.varlse | Roots of characteristic polynomial
stableroot.vharlse | Roots of characteristic polynomial
summary.bvharsp | Summarizing BVAR and BVHAR with Shrinkage Priors
summary.hsmod | Summarizing BVAR and BVHAR with Shrinkage Priors
summary.ngmod | Summarizing BVAR and BVHAR with Shrinkage Priors
summary.normaliw | Summarizing Bayesian Multivariate Time Series Model
summary.ssvsmod | Summarizing BVAR and BVHAR with Shrinkage Priors
summary.varlse | Summarizing Vector Autoregressive Model
summary.vharlse | Summarizing Vector HAR Model

## -- V --

VARtoVMA | Convert VAR to VMA(infinite)
var_bayes | Fitting Bayesian VAR with Coefficient and Covariance Prior
var_lm | Fitting Vector Autoregressive Model of Order p Model
VHARtoVMA | Convert VHAR to VMA(infinite)
vhar_bayes | Fitting Bayesian VHAR with Coefficient and Covariance Prior
vhar_lm | Fitting Vector Heterogeneous Autoregressive Model