Stochastic Search Variable Selection (SSVS) Prior

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.
har: 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()
- By default, use a default semi-automatic approach using choose_ssvs().
init_spec: Gibbs sampler initialization by init_ssvs().
- By default, init_ssvs(type = "auto") uses OLS.
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 both Eigen computation and parallel multi-chain loop
- This option is valid only when OpenMP in user’s machine.

(fit_ssvs <- bvhar_ssvs(etf_train, num_chains = 1, num_iter = 20, include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_ssvs(y = etf_train, num_chains = 1, num_iter = 20, include_mean = FALSE, 
#>     minnesota = "longrun")
#> 
#> BVHAR with SSVS Prior
#> Fitted by Gibbs sampling
#> Total number of iteration: 20
#> Number of burn-in: 10
#> ====================================================
#> 
#> Parameter Record:
#> # A draws_df: 10 iterations, 1 chains, and 63 variables
#>     phi[1]    phi[2]  phi[3]    phi[4]  phi[5]    phi[6]    phi[7]    phi[8]
#> 1    0.368  -0.00254   0.217  -0.00659  0.1339   0.04204   0.01909   0.01827
#> 2    0.468   0.01488   0.146   0.01540  0.2228   0.02630  -0.07248  -0.00927
#> 3    0.609   0.00387   0.172   0.00145  0.1130  -0.00280  -0.04074  -0.00871
#> 4    0.473   0.01275   0.235  -0.03514  0.0814  -0.00769  -0.00534   0.03317
#> 5    0.525   0.01106   0.209  -0.02084  0.1746  -0.01760  -0.01623  -0.02526
#> 6    0.510  -0.01942   0.268   0.01555  0.1615  -0.01459  -0.10195   0.00161
#> 7    0.519   0.00428   0.218   0.00403  0.1053   0.00976  -0.06733   0.04154
#> 8    0.596  -0.01144   0.143  -0.00398  0.1405   0.01432   0.02307  -0.00685
#> 9    0.486   0.00996   0.123   0.02278  0.1969   0.00884  -0.05706  -0.01282
#> 10   0.480  -0.02574   0.270  -0.03183  0.1549  -0.02135  -0.04120   0.02119
#> # ... with 55 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

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 <- bvhar_horseshoe(etf_train, num_chains = 2, num_iter = 20, include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_horseshoe(y = etf_train, num_chains = 2, num_iter = 20, 
#>     include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with Horseshoe Prior
#> Fitted by blocked sampling
#> Number of chains: 2
#> Total number of iteration: 20
#> Number of burn-in: 10
#> ====================================================
#> 
#> # A draws_df: 10 iterations, 2 chains, and 61 variables
#>       phi[1]     phi[2]    phi[3]    phi[4]     phi[5]    phi[6]    phi[7]
#> 1   5.18e-08   1.81e-06  1.51e-04  1.33e-02   4.65e-07  1.08e-03  2.10e-04
#> 2   1.32e-08   2.41e-08  6.55e-06  5.07e-03   2.99e-08  1.51e-03  4.55e-05
#> 3   5.90e-09   3.86e-09  6.53e-07  1.33e-02   8.84e-10  1.30e-06  1.77e-06
#> 4   3.21e-09   2.17e-08  2.52e-07  1.71e-03   1.95e-09  2.25e-05  9.13e-07
#> 5   9.58e-09   2.64e-10  1.61e-06  1.08e-03   4.20e-11  8.90e-07  1.26e-07
#> 6   6.16e-09   3.09e-12  1.42e-05  3.68e-02   3.04e-13  1.30e-05  1.67e-06
#> 7   1.07e-08  -2.40e-14  8.60e-07  4.59e-02   5.47e-13  4.64e-07  7.17e-07
#> 8   3.51e-09   6.67e-13  6.98e-07  7.03e-04  -5.61e-13  2.17e-06  1.95e-08
#> 9   6.72e-12   2.13e-13  2.06e-08  9.49e-05  -2.28e-13  1.77e-07  1.68e-08
#> 10  7.99e-13   5.21e-14  1.26e-09  7.96e-05   1.43e-11  3.26e-07  4.42e-10
#>       phi[8]
#> 1   2.08e-07
#> 2   6.77e-08
#> 3   8.60e-09
#> 4   2.25e-08
#> 5   1.31e-08
#> 6   3.40e-08
#> 7   3.84e-09
#> 8   1.32e-09
#> 9   3.17e-10
#> 10  2.86e-11
#> # ... with 10 more draws, and 53 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot(fit_hs)

Models with Stochastic Volatilities

bvhar_sv() fits VHAR-SV with shrinkage priors.

Three different prior for covariance, and specify through bayes_spec
sv_spec: prior settings for SV, set_sv()

SSVS

(fit_ssvs_sv <- bvhar_sv(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_ssvs(), sv_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_sv(y = etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_ssvs(), 
#>     sv_spec = set_sv(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with Stochastic Volatility
#> Fitted by Gibbs sampling
#> Number of chains: 2
#> Total number of iteration: 20
#> Number of burn-in: 10
#> ====================================================
#> 
#> Parameter Record:
#> # A draws_df: 10 iterations, 2 chains, and 282 variables
#>     phi[1]   phi[2]  phi[3]   phi[4]  phi[5]  phi[6]    phi[7]   phi[8]
#> 1   0.1923  -0.0150  0.0589   0.6196  0.1281   1.246  -0.20680   0.1381
#> 2   0.1916  -0.0904  0.0905   0.1604  0.0959   0.998   0.12531  -0.1326
#> 3   0.1250   0.1351  0.1232  -0.0715  0.2170   1.141  -0.11030   0.0732
#> 4   0.1413   0.0684  0.1015   0.1019  0.0335   1.021  -0.11200   0.0191
#> 5   0.0253   0.2031  0.2272   0.2522  0.1064   1.024   0.05655   0.0395
#> 6   0.0401   0.0835  0.1535  -0.0659  0.1374   0.987   0.10089   0.1364
#> 7   0.0833   0.1005  0.2023   0.0530  0.0677   0.877  -0.00198   0.0529
#> 8   0.1007   0.0625  0.0916  -0.0214  0.0285   0.875   0.07227   0.0386
#> 9   0.2086   0.0284  0.1603  -0.0781  0.1072   0.850   0.05214   0.0480
#> 10  0.1613   0.0654  0.1417   0.0144  0.0362   0.840   0.20474   0.0723
#> # ... with 10 more draws, and 274 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot(fit_ssvs_sv)

Horseshoe

(fit_hs_sv <- bvhar_sv(etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_horseshoe(), sv_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_sv(y = etf_train, num_chains = 2, num_iter = 20, bayes_spec = set_horseshoe(), 
#>     sv_spec = set_sv(), include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with Stochastic Volatility
#> Fitted by Gibbs sampling
#> Number of chains: 2
#> Total number of iteration: 20
#> Number of burn-in: 10
#> ====================================================
#> 
#> Parameter Record:
#> # A draws_df: 10 iterations, 2 chains, and 315 variables
#>      phi[1]    phi[2]    phi[3]   phi[4]    phi[5]   phi[6]   phi[7]   phi[8]
#> 1   1.81170  -0.04887   0.17674   0.1222  -0.96104   0.4752  -1.7864   1.6946
#> 2   0.42250  -0.05241  -0.09456  -0.0695  -0.40474  -0.2182   0.3485   1.2815
#> 3   0.00219  -0.12305   0.00252  -0.1339   0.09801   0.1174   0.5293   0.6035
#> 4   0.40343  -0.08217  -0.05841   0.3230   0.08070   0.0878   0.0715   0.5309
#> 5   0.48051   0.00716  -0.05710   0.1016   0.09021   0.1951   0.0800  -0.2272
#> 6   0.48797   0.03734   0.00408   0.0536   0.05661   0.6725   0.0156   0.4734
#> 7   0.45704   0.01631   0.00222   0.0204  -0.00182   1.1471   0.0322   0.1542
#> 8   0.57873   0.00778   0.03212  -0.2233   0.08151   1.1284  -0.0615   0.0838
#> 9   0.55219   0.00794   0.04163  -0.2964   0.12853   1.1669   0.0321   0.1459
#> 10  0.39159   0.06693  -0.00969  -0.0221   0.18191   1.0690   0.0112  -0.0573
#> # ... with 10 more draws, and 307 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

Bayesian visualization

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

autoplot(fit_hs_sv, 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.