# bvhar

## Overview

`bvhar` provides functions to analyze and forecast multivariate time
series using

- VAR
- VHAR (Vector HAR)
- BVAR (Bayesian VAR)
- **BVHAR (Bayesian VHAR)**

Basically, the package focuses on the research with forecasting.

## Installation

``` r

install.packages("bvhar")
```

### Development version

You can install the development version from [develop
branch](https://github.com/ygeunkim/bvhar/tree/develop).

``` r

# install.packages("remotes")
remotes::install_github("ygeunkim/bvhar@develop")
```

We started to develop a Python version in python directory.

- [bvhar for Python](https://bvhar.baeconverse.org/python/)
- [Source code](https://github.com/ygeunkim/bvhar/tree/master/python)

## Models

``` r

library(bvhar) # this package
library(dplyr)
```

Repeatedly, `bvhar` is a research tool to analyze multivariate time
series model above

| Model | function | prior |
|:--:|:--:|:--:|
| VAR | [`var_lm()`](reference/var_lm.md) |  |
| VHAR | [`vhar_lm()`](reference/vhar_lm.md) |  |
| BVAR | [`bvar_minnesota()`](reference/bvar_minnesota.md) | Minnesota (will move to [`var_bayes()`](reference/var_bayes.md)) |
| BVHAR | [`bvhar_minnesota()`](reference/bvhar_minnesota.md) | Minnesota (will move to [`vhar_bayes()`](reference/vhar_bayes.md)) |
| BVAR | [`var_bayes()`](reference/var_bayes.md) | SSVS, Horseshoe, Minnesota, NG, DL, GDP |
| BVHAR | [`vhar_bayes()`](reference/vhar_bayes.md) | SSVS, Horseshoe, Minnesota, NG, DL, GDP |

This readme document shows forecasting procedure briefly. Details about
each function are in vignettes and help documents. Details will be
updated after the function integration works are done. Until then, we
remove Bayesian model sections here.

h-step ahead forecasting:

``` r

h <- 19
etf_split <- divide_ts(etf_vix, h) # Try ?divide_ts
etf_tr <- etf_split$train
etf_te <- etf_split$test
```

### VAR

VAR(5):

``` r

mod_var <- var_lm(y = etf_tr, p = 5)
```

Forecasting:

``` r

forecast_var <- predict(mod_var, h)
```

MSE:

``` r

(msevar <- mse(forecast_var, etf_te))
#>   GVZCLS   OVXCLS VXFXICLS VXEEMCLS VXSLVCLS   EVZCLS VXXLECLS VXGDXCLS 
#>    5.381   14.689    2.838    9.451   10.078    0.654   22.436    9.992 
#> VXEWZCLS 
#>   10.647
```

### VHAR

``` r

mod_vhar <- vhar_lm(y = etf_tr)
```

MSE:

``` r

forecast_vhar <- predict(mod_vhar, h)
(msevhar <- mse(forecast_vhar, etf_te))
#>   GVZCLS   OVXCLS VXFXICLS VXEEMCLS VXSLVCLS   EVZCLS VXXLECLS VXGDXCLS 
#>     6.15     2.49     1.52     1.58    10.55     1.35     8.79     4.43 
#> VXEWZCLS 
#>     3.84
```

### BVAR

### BVHAR

## Citation

Please cite this package with following BibTeX:

``` R
@Manual{,
  title = {{bvhar}: Bayesian Vector Heterogeneous Autoregressive Modeling},
  author = {Young Geun Kim and Changryong Baek},
  year = {2023},
  doi = {10.32614/CRAN.package.bvhar},
  note = {R package version 2.4.1},
  url = {https://cran.r-project.org/package=bvhar},
}

@Article{,
  title = {Bayesian Vector Heterogeneous Autoregressive Modeling},
  author = {Young Geun Kim and Changryong Baek},
  journal = {Journal of Statistical Computation and Simulation},
  year = {2024},
  volume = {94},
  number = {6},
  pages = {1139--1157},
  doi = {10.1080/00949655.2023.2281644},
}
```

## Code of Conduct

Please note that the bvhar project is released with a [Contributor Code
of
Conduct](https://contributor-covenant.org/version/2/0/CODE_OF_CONDUCT.html).
By contributing to this project, you agree to abide by its terms.

# Package index

## Package

The bvhar package

- [`bvhar`](bvhar-package.md) [`bvhar-package`](bvhar-package.md) :
  bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

## Frequentist modeling

Vector autoregressive (VAR) and heterogeneous autoregressive (VHAR)
models.

- [`var_lm()`](var_lm.md) [`print(`*`<varlse>`*`)`](var_lm.md)
  [`logLik(`*`<varlse>`*`)`](var_lm.md)
  [`AIC(`*`<varlse>`*`)`](var_lm.md) [`BIC(`*`<varlse>`*`)`](var_lm.md)
  [`is.varlse()`](var_lm.md) [`is.bvharmod()`](var_lm.md)
  [`knit_print(`*`<varlse>`*`)`](var_lm.md) : Fitting Vector
  Autoregressive Model of Order p Model
- [`vhar_lm()`](vhar_lm.md) [`print(`*`<vharlse>`*`)`](vhar_lm.md)
  [`logLik(`*`<vharlse>`*`)`](vhar_lm.md)
  [`AIC(`*`<vharlse>`*`)`](vhar_lm.md)
  [`BIC(`*`<vharlse>`*`)`](vhar_lm.md) [`is.vharlse()`](vhar_lm.md)
  [`knit_print(`*`<vharlse>`*`)`](vhar_lm.md) : Fitting Vector
  Heterogeneous Autoregressive Model
- [`VARtoVMA()`](VARtoVMA.md) : Convert VAR to VMA(infinite)
- [`VHARtoVMA()`](VHARtoVMA.md) : Convert VHAR to VMA(infinite)
- [`summary(`*`<varlse>`*`)`](summary.varlse.md)
  [`print(`*`<summary.varlse>`*`)`](summary.varlse.md)
  [`knit_print(`*`<summary.varlse>`*`)`](summary.varlse.md) :
  Summarizing Vector Autoregressive Model
- [`summary(`*`<vharlse>`*`)`](summary.vharlse.md)
  [`print(`*`<summary.vharlse>`*`)`](summary.vharlse.md)
  [`knit_print(`*`<summary.vharlse>`*`)`](summary.vharlse.md) :
  Summarizing Vector HAR Model

## Prior specification

Prior settings for Bayesian models.

- [`set_bvar()`](set_bvar.md) [`set_bvar_flat()`](set_bvar.md)
  [`set_bvhar()`](set_bvar.md) [`set_weight_bvhar()`](set_bvar.md)
  [`print(`*`<bvharspec>`*`)`](set_bvar.md)
  [`is.bvharspec()`](set_bvar.md)
  [`knit_print(`*`<bvharspec>`*`)`](set_bvar.md) : Hyperparameters for
  Bayesian Models
- [`set_ssvs()`](set_ssvs.md) [`print(`*`<ssvsinput>`*`)`](set_ssvs.md)
  [`is.ssvsinput()`](set_ssvs.md)
  [`knit_print(`*`<ssvsinput>`*`)`](set_ssvs.md) : Stochastic Search
  Variable Selection (SSVS) Hyperparameter for Coefficients Matrix and
  Cholesky Factor
- [`set_lambda()`](set_lambda.md) [`set_psi()`](set_lambda.md)
  [`print(`*`<bvharpriorspec>`*`)`](set_lambda.md)
  [`is.bvharpriorspec()`](set_lambda.md)
  [`knit_print(`*`<bvharpriorspec>`*`)`](set_lambda.md) : Hyperpriors
  for Bayesian Models
- [`set_horseshoe()`](set_horseshoe.md)
  [`print(`*`<horseshoespec>`*`)`](set_horseshoe.md)
  [`is.horseshoespec()`](set_horseshoe.md)
  [`knit_print(`*`<horseshoespec>`*`)`](set_horseshoe.md) : Horseshoe
  Prior Specification
- [`set_ng()`](set_ng.md) [`print(`*`<ngspec>`*`)`](set_ng.md)
  [`is.ngspec()`](set_ng.md) **\[experimental\]** : Normal-Gamma
  Hyperparameter for Coefficients and Contemporaneous Coefficients
- [`set_dl()`](set_dl.md) [`print(`*`<dlspec>`*`)`](set_dl.md)
  [`is.dlspec()`](set_dl.md) **\[experimental\]** : Dirichlet-Laplace
  Hyperparameter for Coefficients and Contemporaneous Coefficients
- [`set_gdp()`](set_gdp.md) [`is.gdpspec()`](set_gdp.md)
  **\[experimental\]** : Generalized Double Pareto Shrinkage
  Hyperparameters for Coefficients and Contemporaneous Coefficients
- [`set_ldlt()`](set_ldlt.md) [`set_sv()`](set_ldlt.md)
  [`print(`*`<covspec>`*`)`](set_ldlt.md) [`is.covspec()`](set_ldlt.md)
  [`is.svspec()`](set_ldlt.md) [`is.ldltspec()`](set_ldlt.md)
  **\[experimental\]** : Covariance Matrix Prior Specification
- [`set_factor()`](set_factor.md) **\[experimental\]** : Factor
  Specification
- [`set_intercept()`](set_intercept.md)
  [`print(`*`<interceptspec>`*`)`](set_intercept.md)
  [`is.interceptspec()`](set_intercept.md)
  [`knit_print(`*`<interceptspec>`*`)`](set_intercept.md) : Prior for
  Constant Term

## Bayesian modeling

Bayesian VAR and Bayesian VHAR models.

- [`var_bayes()`](var_bayes.md) [`print(`*`<bvarsv>`*`)`](var_bayes.md)
  [`print(`*`<bvarldlt>`*`)`](var_bayes.md)
  [`knit_print(`*`<bvarsv>`*`)`](var_bayes.md)
  [`knit_print(`*`<bvarldlt>`*`)`](var_bayes.md) **\[maturing\]** :
  Fitting Bayesian VAR with Coefficient and Covariance Prior
- [`bvar_minnesota()`](bvar_minnesota.md)
  [`print(`*`<bvarmn>`*`)`](bvar_minnesota.md)
  [`print(`*`<bvarhm>`*`)`](bvar_minnesota.md)
  [`logLik(`*`<bvarmn>`*`)`](bvar_minnesota.md)
  [`AIC(`*`<bvarmn>`*`)`](bvar_minnesota.md)
  [`BIC(`*`<bvarmn>`*`)`](bvar_minnesota.md)
  [`is.bvarmn()`](bvar_minnesota.md)
  [`knit_print(`*`<bvarmn>`*`)`](bvar_minnesota.md)
  [`knit_print(`*`<bvarhm>`*`)`](bvar_minnesota.md) : Fitting Bayesian
  VAR(p) of Minnesota Prior
- [`bvar_flat()`](bvar_flat.md)
  [`print(`*`<bvarflat>`*`)`](bvar_flat.md)
  [`logLik(`*`<bvarflat>`*`)`](bvar_flat.md)
  [`AIC(`*`<bvarflat>`*`)`](bvar_flat.md)
  [`BIC(`*`<bvarflat>`*`)`](bvar_flat.md)
  [`is.bvarflat()`](bvar_flat.md)
  [`knit_print(`*`<bvarflat>`*`)`](bvar_flat.md) : Fitting Bayesian
  VAR(p) of Flat Prior
- [`vhar_bayes()`](vhar_bayes.md)
  [`print(`*`<bvharsv>`*`)`](vhar_bayes.md)
  [`print(`*`<bvharldlt>`*`)`](vhar_bayes.md)
  [`knit_print(`*`<bvharsv>`*`)`](vhar_bayes.md)
  [`knit_print(`*`<bvharldlt>`*`)`](vhar_bayes.md) **\[maturing\]** :
  Fitting Bayesian VHAR with Coefficient and Covariance Prior
- [`bvhar_minnesota()`](bvhar_minnesota.md)
  [`print(`*`<bvharmn>`*`)`](bvhar_minnesota.md)
  [`print(`*`<bvharhm>`*`)`](bvhar_minnesota.md)
  [`logLik(`*`<bvharmn>`*`)`](bvhar_minnesota.md)
  [`AIC(`*`<bvharmn>`*`)`](bvhar_minnesota.md)
  [`BIC(`*`<bvharmn>`*`)`](bvhar_minnesota.md)
  [`is.bvharmn()`](bvhar_minnesota.md)
  [`knit_print(`*`<bvharmn>`*`)`](bvhar_minnesota.md)
  [`knit_print(`*`<bvharhm>`*`)`](bvhar_minnesota.md) : Fitting Bayesian
  VHAR of Minnesota Prior
- [`summary(`*`<normaliw>`*`)`](summary.normaliw.md)
  [`print(`*`<summary.normaliw>`*`)`](summary.normaliw.md)
  [`knit_print(`*`<summary.normaliw>`*`)`](summary.normaliw.md) :
  Summarizing Bayesian Multivariate Time Series Model
- [`print(`*`<summary.bvharsp>`*`)`](summary.bvharsp.md)
  [`knit_print(`*`<summary.bvharsp>`*`)`](summary.bvharsp.md)
  [`summary(`*`<ssvsmod>`*`)`](summary.bvharsp.md)
  [`summary(`*`<hsmod>`*`)`](summary.bvharsp.md)
  [`summary(`*`<ngmod>`*`)`](summary.bvharsp.md) : Summarizing BVAR and
  BVHAR with Shrinkage Priors

## Deprecated

Deprecated functions that will be removed soon

- [`choose_bvar()`](choose_bvar.md) [`choose_bvhar()`](choose_bvar.md)
  [`print(`*`<bvharemp>`*`)`](choose_bvar.md)
  [`is.bvharemp()`](choose_bvar.md)
  [`knit_print(`*`<bvharemp>`*`)`](choose_bvar.md) **\[deprecated\]** :
  Finding the Set of Hyperparameters of Individual Bayesian Model
- [`bound_bvhar()`](bound_bvhar.md)
  [`print(`*`<boundbvharemp>`*`)`](bound_bvhar.md)
  [`is.boundbvharemp()`](bound_bvhar.md)
  [`knit_print(`*`<boundbvharemp>`*`)`](bound_bvhar.md)
  **\[deprecated\]** : Setting Empirical Bayes Optimization Bounds
- [`choose_bayes()`](choose_bayes.md) **\[deprecated\]** : Finding the
  Set of Hyperparameters of Bayesian Model

## Forecasting

- [`predict(`*`<varlse>`*`)`](predict.md)
  [`predict(`*`<vharlse>`*`)`](predict.md)
  [`predict(`*`<bvarmn>`*`)`](predict.md)
  [`predict(`*`<bvharmn>`*`)`](predict.md)
  [`predict(`*`<bvarflat>`*`)`](predict.md)
  [`predict(`*`<bvarldlt>`*`)`](predict.md)
  [`predict(`*`<bvharldlt>`*`)`](predict.md)
  [`predict(`*`<bvarsv>`*`)`](predict.md)
  [`predict(`*`<bvharsv>`*`)`](predict.md)
  [`print(`*`<predbvhar>`*`)`](predict.md)
  [`is.predbvhar()`](predict.md)
  [`knit_print(`*`<predbvhar>`*`)`](predict.md) : Forecasting
  Multivariate Time Series
- [`divide_ts()`](divide_ts.md) : Split a Time Series Dataset into
  Train-Test Set
- [`forecast_roll()`](forecast_roll.md)
  [`print(`*`<bvharcv>`*`)`](forecast_roll.md)
  [`is.bvharcv()`](forecast_roll.md)
  [`knit_print(`*`<bvharcv>`*`)`](forecast_roll.md) : Out-of-sample
  Forecasting based on Rolling Window
- [`forecast_expand()`](forecast_expand.md) : Out-of-sample Forecasting
  based on Expanding Window

## Structural analysis

- [`print(`*`<bvharirf>`*`)`](irf.md) [`irf()`](irf.md)
  [`is.bvharirf()`](irf.md) [`knit_print(`*`<bvharirf>`*`)`](irf.md) :
  Impulse Response Analysis
- [`spillover()`](spillover.md)
  [`print(`*`<bvharspillover>`*`)`](spillover.md)
  [`knit_print(`*`<bvharspillover>`*`)`](spillover.md) : h-step ahead
  Normalized Spillover
- [`dynamic_spillover()`](dynamic_spillover.md)
  [`print(`*`<bvhardynsp>`*`)`](dynamic_spillover.md)
  [`knit_print(`*`<bvhardynsp>`*`)`](dynamic_spillover.md) : Dynamic
  Spillover

## Evaluation

- [`mse()`](mse.md) : Evaluate the Model Based on MSE (Mean Square
  Error)
- [`mae()`](mae.md) : Evaluate the Model Based on MAE (Mean Absolute
  Error)
- [`mape()`](mape.md) : Evaluate the Model Based on MAPE (Mean Absolute
  Percentage Error)
- [`mase()`](mase.md) : Evaluate the Model Based on MASE (Mean Absolute
  Scaled Error)
- [`mrae()`](mrae.md) : Evaluate the Model Based on MRAE (Mean Relative
  Absolute Error)
- [`alpl()`](alpl.md) : Evaluate the Density Forecast Based on Average
  Log Predictive Likelihood (APLP)
- [`relmae()`](relmae.md) : Evaluate the Model Based on RelMAE (Relative
  MAE)
- [`rmsfe()`](rmsfe.md) : Evaluate the Model Based on RMSFE
- [`rmafe()`](rmafe.md) : Evaluate the Model Based on RMAFE
- [`rmape()`](rmape.md) : Evaluate the Model Based on RMAPE (Relative
  MAPE)
- [`rmase()`](rmase.md) : Evaluate the Model Based on RMASE (Relative
  MASE)
- [`conf_fdr()`](conf_fdr.md) : Evaluate the Sparsity Estimation Based
  on FDR
- [`conf_fnr()`](conf_fnr.md) : Evaluate the Sparsity Estimation Based
  on FNR
- [`conf_fscore()`](conf_fscore.md) : Evaluate the Sparsity Estimation
  Based on F1 Score
- [`conf_prec()`](conf_prec.md) : Evaluate the Sparsity Estimation Based
  on Precision
- [`conf_recall()`](conf_recall.md) : Evaluate the Sparsity Estimation
  Based on Recall
- [`confusion()`](confusion.md) : Evaluate the Sparsity Estimation Based
  on Confusion Matrix
- [`fromse()`](fromse.md) : Evaluate the Estimation Based on Frobenius
  Norm
- [`spne()`](spne.md) : Evaluate the Estimation Based on Spectral Norm
  Error
- [`relspne()`](relspne.md) : Evaluate the Estimation Based on Relative
  Spectral Norm Error
- [`compute_logml()`](compute_logml.md) : Extracting Log of Marginal
  Likelihood
- [`FPE()`](FPE.md) : Final Prediction Error Criterion
- [`HQ()`](HQ.md) : Hannan-Quinn Criterion
- [`choose_var()`](choose_var.md) : Choose the Best VAR based on
  Information Criteria
- [`compute_dic()`](compute_dic.md) : Deviance Information Criterion of
  Multivariate Time Series Model

## Plots

- [`autoplot(`*`<normaliw>`*`)`](autoplot.normaliw.md) : Residual Plot
  for Minnesota Prior VAR Model
- [`autoplot(`*`<summary.normaliw>`*`)`](autoplot.summary.normaliw.md) :
  Density Plot for Minnesota Prior VAR Model
- [`autoplot(`*`<predbvhar>`*`)`](autoplot.predbvhar.md)
  [`autolayer(`*`<predbvhar>`*`)`](autoplot.predbvhar.md) : Plot
  Forecast Result
- [`geom_eval()`](geom_eval.md) : Adding Test Data Layer
- [`gg_loss()`](gg_loss.md) : Compare Lists of Models
- [`autoplot(`*`<bvharirf>`*`)`](autoplot.bvharirf.md) : Plot Impulse
  Responses
- [`autoplot(`*`<bvharsp>`*`)`](autoplot.bvharsp.md) : Plot the Result
  of BVAR and BVHAR MCMC
- [`autoplot(`*`<summary.bvharsp>`*`)`](autoplot.summary.bvharsp.md) :
  Plot the Heatmap of SSVS Coefficients
- [`autoplot(`*`<bvhardynsp>`*`)`](autoplot.bvhardynsp.md) : Dynamic
  Spillover Indices Plot

## Simulation and Random Generation

- [`sim_var()`](sim_var.md) : Generate Multivariate Time Series Process
  Following VAR(p)
- [`sim_vhar()`](sim_vhar.md) : Generate Multivariate Time Series
  Process Following VAR(p)
- [`sim_mncoef()`](sim_mncoef.md) : Generate Minnesota BVAR Parameters
- [`sim_mnvhar_coef()`](sim_mnvhar_coef.md) : Generate Minnesota BVAR
  Parameters
- [`sim_mnormal()`](sim_mnormal.md) : Generate Multivariate Normal
  Random Vector
- [`sim_matgaussian()`](sim_matgaussian.md) : Generate Matrix Normal
  Random Matrix
- [`sim_iw()`](sim_iw.md) : Generate Inverse-Wishart Random Matrix
- [`sim_mniw()`](sim_mniw.md) : Generate Normal-IW Random Family
- [`sim_mvt()`](sim_mvt.md) : Generate Multivariate t Random Vector

## Data

- [`etf_vix`](etf_vix.md) : CBOE ETF Volatility Index Dataset

## Other generic functions

- [`stableroot()`](stableroot.md) : Roots of characteristic polynomial
- [`is.stable()`](is.stable.md) : Stability of the process
- [`coef(`*`<varlse>`*`)`](coef.md) [`coef(`*`<vharlse>`*`)`](coef.md)
  [`coef(`*`<bvarmn>`*`)`](coef.md) [`coef(`*`<bvarflat>`*`)`](coef.md)
  [`coef(`*`<bvharmn>`*`)`](coef.md) [`coef(`*`<bvharsp>`*`)`](coef.md)
  [`coef(`*`<summary.bvharsp>`*`)`](coef.md) : Coefficient Matrix of
  Multivariate Time Series Models
- [`residuals(`*`<varlse>`*`)`](residuals.md)
  [`residuals(`*`<vharlse>`*`)`](residuals.md)
  [`residuals(`*`<bvarmn>`*`)`](residuals.md)
  [`residuals(`*`<bvarflat>`*`)`](residuals.md)
  [`residuals(`*`<bvharmn>`*`)`](residuals.md) : Residual Matrix from
  Multivariate Time Series Models
- [`fitted(`*`<varlse>`*`)`](fitted.md)
  [`fitted(`*`<vharlse>`*`)`](fitted.md)
  [`fitted(`*`<bvarmn>`*`)`](fitted.md)
  [`fitted(`*`<bvarflat>`*`)`](fitted.md)
  [`fitted(`*`<bvharmn>`*`)`](fitted.md) : Fitted Matrix from
  Multivariate Time Series Models

# Articles

### All vignettes

- [Introduction to bvhar](bvhar.md):
- [Forecasting](forecasting.md):
- [Minnesota Prior](minnesota.md):
- [Bayesian VAR and VHAR Models](shrinkage.md):
- [Stochastic Volatility Models](stochastic-volatility.md):