Bayesian Vector Heterogeneous Autoregressive Modeling • bvhar

Overview

bvhar provides functions to analyze multivariate time series 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")

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
BVHAR	`bvhar_minnesota()`	Minnesota
BVAR-SV	`bvar_sv()`	SSVS, Horseshoe
BVHAR-SV	`bvhar_sv()`	SSVS, Horseshoe

This readme document shows forecasting procedure briefly. Details about each function are in vignettes and help documents.

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
#> # Type '?bvar_minnesota' in the console for some help.
#> ========================================================
#> 
#> 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

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 
#>    4.463   13.510    1.336   11.267    9.802    0.862   21.929    5.418 
#> VXEWZCLS 
#>    7.362

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
#> # Type '?bvhar_minnesota' in the console for some help.
#> ========================================================
#> 
#> 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

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 
#>     3.58     4.76     1.32     5.71     6.29     1.15    14.03     2.52 
#> VXEWZCLS 
#>     5.41

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
#> # Type '?bvhar_minnesota' in the console for some help.
#> ========================================================
#> 
#> 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

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     4.39     1.37     5.63     6.16     1.19    14.18     2.52 
#> VXEWZCLS 
#>     5.23

Plots

autoplot(forecast_var, x_cut = 870, ci_alpha = .7, type = "wrap") +
  autolayer(forecast_vhar, ci_alpha = .6) +
  autolayer(forecast_bvar, ci_alpha = .4) +
  autolayer(forecast_bvhar_v1, ci_alpha = .2) +
  autolayer(forecast_bvhar_v2, ci_alpha = .1)

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},
  note = {R package version 2.0.1},
  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 = {2023},
  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.