Bayesian VAR and VHAR Models

In bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

knitr::opts_chunk$set(
  comment = "#>",
  collapse = TRUE,
  out.width = "70%",
  fig.align = "center",
  fig.width = 6,
  fig.asp = .618
)
orig_opts <- options("digits")
options(digits = 3)
set.seed(1)

library(bvhar)

etf <- etf_vix[1:55, 1:3]
# Split-------------------------------
h <- 5
etf_eval <- divide_ts(etf, h)
etf_train <- etf_eval$train
etf_test <- etf_eval$test

Bayesian VAR and VHAR

var_bayes() and vhar_bayes() fit BVAR and BVHAR each with various priors.

• y: Multivariate time series data. It should be data frame or matrix, which means that every column is numeric. Each column indicates variable, i.e. it sould be wide format.
• p or har: VAR lag, or order of VHAR
• num_chains: Number of chains
  • If OpenMP is enabled, parallel loop will be run.
• num_iter: Total number of iterations
• num_burn: Number of burn-in
• thinning: Thinning
• bayes_spec: Output of set_ssvs()
  • Minneosta prior
    • BVAR: set_bvar()
    • BVHAR: set_bvhar() and set_weight_bvhar()
    • Can induce prior on $\lambda$ using lambda = set_lambda()
  • SSVS prior: set_ssvs()
  • Horseshoe prior: set_horseshoe()
  • NG prior: set_ng()
  • DL prior: set_dl()
• cov_spec: Covariance prior specification. Use set_ldlt() for homoskedastic model.
• include_mean = TRUE: By default, you include the constant term in the model.
• minnesota = c("no", "short", "longrun"): Minnesota-type shrinkage.
• verbose = FALSE: Progress bar
• num_thread: Number of thread for OpenMP
  • Used in parallel multi-chain loop
  • This option is valid only when OpenMP in user's machine.

Stochastic Search Variable Selection (SSVS) Prior

(fit_ssvs <- vhar_bayes(etf_train, num_chains = 1, num_iter = 20, bayes_spec = set_ssvs(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))

autoplot() for the fit (bvharsp object) provides coefficients heatmap. There is type argument, and the default type = "coef" draws the heatmap.

autoplot(fit_ssvs)

Horseshoe Prior

bayes_spec is the initial specification by set_horseshoe(). Others are the same.

(fit_hs <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_horseshoe(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))

autoplot(fit_hs)

Minnesota Prior

(fit_mn <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_bvhar(lambda = set_lambda()), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))

Normal-Gamma prior

(fit_ng <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_ng(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))

Dirichlet-Laplace prior

(fit_dl <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_dl(), cov_spec = set_ldlt(), include_mean = FALSE, minnesota = "longrun"))

Bayesian visualization

autoplot() also provides Bayesian visualization. type = "trace" gives MCMC trace plot.

autoplot(fit_hs, type = "trace", regex_pars = "tau")

type = "dens" draws MCMC density plot. If specifying additional argument facet_args = list(dir = "v") of bayesplot, you can see plot as the same format with coefficient matrix.

autoplot(fit_hs, type = "dens", regex_pars = "kappa", facet_args = list(dir = "v", nrow = nrow(fit_hs$coefficients)))

options(orig_opts)

bvhar documentation built on April 4, 2025, 5:22 a.m.