Stochastic Volatility 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

Models with Stochastic Volatilities

By specifying cov_spec = set_sv(), var_bayes() and vhar_bayes() fits VAR-SV and VHAR-SV with shrinkage priors, respectively.

• Three different prior for innovation covariance, and specify through bayes_spec
  • Minneosta prior
    • BVAR: set_bvar()
    • BVHAR: set_bvhar() and set_weight_bvhar()
  • SSVS prior: set_ssvs()
  • Horseshoe prior: set_horseshoe()
  • NG prior: set_ng()
  • DL prior: set_dl()
• sv_spec: prior settings for SV, set_sv()
• intercept: prior for constant term, set_intercept()

set_sv()

SSVS

(fit_ssvs <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_ssvs(), cov_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))

Horseshoe

(fit_hs <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_horseshoe(), cov_spec = set_sv(), 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_sv(), 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_sv(), 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.

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

options(orig_opts)

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