Bayesian Vector Heterogeneous Autoregressive Modeling • 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

install.packages("bvhar")

Development version

You can install the development version from develop branch.

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

We started to develop a Python version in python directory.

Models

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()`
VHAR	`vhar_lm()`
BVAR	`bvar_minnesota()`	Minnesota (will move to `var_bayes()`)
BVHAR	`bvhar_minnesota()`	Minnesota (will move to `vhar_bayes()`)
BVAR	`var_bayes()`	SSVS, Horseshoe, Minnesota, NG, DL
BVHAR	`vhar_bayes()`	SSVS, Horseshoe, Minnesota, NG, DL

This readme document shows forecasting procedure briefly. Details about each function are in vignettes and help documents. Note that each bvar_minnesota() and bvhar_minnesota() will be integrated into var_bayes() and vhar_bayes() and removed in the next version.

h-step ahead forecasting:

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):

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

Forecasting:

forecast_var <- predict(mod_var, h)

MSE:

(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

mod_vhar <- vhar_lm(y = etf_tr)

MSE:

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

Minnesota prior:

lam <- .3
delta <- rep(1, ncol(etf_vix)) # litterman
sig <- apply(etf_tr, 2, sd)
eps <- 1e-04
(bvar_spec <- set_bvar(sig, lam, delta, eps))
#> Model Specification for BVAR
#> 
#> Parameters: Coefficent matrice and Covariance matrix
#> Prior: Minnesota
#> ========================================================
#> 
#> Setting for 'sigma':
#>   GVZCLS    OVXCLS  VXFXICLS  VXEEMCLS  VXSLVCLS    EVZCLS  VXXLECLS  VXGDXCLS  
#>     3.77     10.63      3.81      4.39      5.99      2.27      4.88      7.45  
#> VXEWZCLS  
#>     7.03  
#> 
#> Setting for 'lambda':
#> [1]  0.3
#> 
#> Setting for 'delta':
#> [1]  1  1  1  1  1  1  1  1  1
#> 
#> Setting for 'eps':
#> [1]  1e-04
#> 
#> Setting for 'hierarchical':
#> [1]  FALSE

mod_bvar <- bvar_minnesota(y = etf_tr, p = 5, bayes_spec = bvar_spec)

MSE:

forecast_bvar <- predict(mod_bvar, h)
(msebvar <- mse(forecast_bvar, etf_te))
#>   GVZCLS   OVXCLS VXFXICLS VXEEMCLS VXSLVCLS   EVZCLS VXXLECLS VXGDXCLS 
#>    4.651   13.248    1.845   10.356    9.894    0.667   21.040    6.262 
#> VXEWZCLS 
#>    8.864

BVHAR

BVHAR-S:

(bvhar_spec_v1 <- set_bvhar(sig, lam, delta, eps))
#> Model Specification for BVHAR
#> 
#> Parameters: Coefficent matrice and Covariance matrix
#> Prior: MN_VAR
#> ========================================================
#> 
#> Setting for 'sigma':
#>   GVZCLS    OVXCLS  VXFXICLS  VXEEMCLS  VXSLVCLS    EVZCLS  VXXLECLS  VXGDXCLS  
#>     3.77     10.63      3.81      4.39      5.99      2.27      4.88      7.45  
#> VXEWZCLS  
#>     7.03  
#> 
#> Setting for 'lambda':
#> [1]  0.3
#> 
#> Setting for 'delta':
#> [1]  1  1  1  1  1  1  1  1  1
#> 
#> Setting for 'eps':
#> [1]  1e-04
#> 
#> Setting for 'hierarchical':
#> [1]  FALSE

mod_bvhar_v1 <- bvhar_minnesota(y = etf_tr, bayes_spec = bvhar_spec_v1)

MSE:

forecast_bvhar_v1 <- predict(mod_bvhar_v1, h)
(msebvhar_v1 <- mse(forecast_bvhar_v1, etf_te))
#>   GVZCLS   OVXCLS VXFXICLS VXEEMCLS VXSLVCLS   EVZCLS VXXLECLS VXGDXCLS 
#>    3.199    6.067    1.471    5.142    5.946    0.878   12.165    2.553 
#> VXEWZCLS 
#>    6.462

BVHAR-L:

day <- rep(.1, ncol(etf_vix))
week <- rep(.1, ncol(etf_vix))
month <- rep(.1, ncol(etf_vix))
#----------------------------------
(bvhar_spec_v2 <- set_weight_bvhar(sig, lam, eps, day, week, month))
#> Model Specification for BVHAR
#> 
#> Parameters: Coefficent matrice and Covariance matrix
#> Prior: MN_VHAR
#> ========================================================
#> 
#> Setting for 'sigma':
#>   GVZCLS    OVXCLS  VXFXICLS  VXEEMCLS  VXSLVCLS    EVZCLS  VXXLECLS  VXGDXCLS  
#>     3.77     10.63      3.81      4.39      5.99      2.27      4.88      7.45  
#> VXEWZCLS  
#>     7.03  
#> 
#> Setting for 'lambda':
#> [1]  0.3
#> 
#> Setting for 'eps':
#> [1]  1e-04
#> 
#> Setting for 'daily':
#> [1]  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1
#> 
#> Setting for 'weekly':
#> [1]  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1
#> 
#> Setting for 'monthly':
#> [1]  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1  0.1
#> 
#> Setting for 'hierarchical':
#> [1]  FALSE

mod_bvhar_v2 <- bvhar_minnesota(y = etf_tr, bayes_spec = bvhar_spec_v2)

MSE:

forecast_bvhar_v2 <- predict(mod_bvhar_v2, h)
(msebvhar_v2 <- mse(forecast_bvhar_v2, etf_te))
#>   GVZCLS   OVXCLS VXFXICLS VXEEMCLS VXSLVCLS   EVZCLS VXXLECLS VXGDXCLS 
#>     3.63     3.85     1.64     5.12     5.75     1.08    13.60     2.58 
#> VXEWZCLS 
#>     5.54

Citation

Please cite this package with following BibTeX:

@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 2.1.1},
  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. By contributing to this project, you agree to abide by its terms.