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_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

(fit_ssvs <- bvhar_ssvs(etf_train, num_iter = 50, include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_ssvs(y = etf_train, num_iter = 50, include_mean = FALSE, 
#>     minnesota = "longrun")
#> 
#> BVHAR with SSVS Prior
#> Fitted by Gibbs sampling
#> Total number of iteration: 50
#> Number of burn-in: 25
#> ====================================================
#> 
#> Parameter Record:
#> # A draws_df: 25 iterations, 1 chains, and 112 variables
#>     phi[1]    phi[2]   phi[3]     phi[4]    phi[5]    phi[6]    phi[7]   phi[8]
#> 1    0.698  -0.00226  -0.0123   0.037430   0.02887   0.03234   0.04147  0.00751
#> 2    0.873   0.02821   0.0360   0.010323   0.04918   0.01284   0.03641  0.00163
#> 3    0.763   0.01056  -0.0212  -0.000826  -0.02758   0.01102   0.05360  0.04717
#> 4    0.889   0.00357  -0.0204   0.034986  -0.00416  -0.02446  -0.03122  0.02264
#> 5    0.859   0.01599   0.0599   0.029510   0.01150   0.00536   0.00188  0.00865
#> 6    0.956  -0.01873   0.0263   0.003166   0.02746   0.05086  -0.00259  0.00709
#> 7    0.782   0.00567   0.0208   0.009171   0.01129   0.03717  -0.07532  0.00518
#> 8    0.817   0.03570   0.0362   0.003582   0.03489  -0.00423   0.03803  0.02531
#> 9    0.932   0.00745  -0.0411   0.010844   0.01799   0.01914   0.10273  0.01348
#> 10   0.740   0.04380   0.0326   0.016294  -0.01817   0.02164   0.02196  0.00779
#> # ... with 15 more draws, and 104 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)

type = "trace" gives MCMC trace plot.

autoplot(fit_ssvs, type = "trace", regex_pars = "psi")

Horseshoe Prior

(fit_hs <- bvhar_horseshoe(etf_train, num_iter = 50, include_mean = FALSE, minnesota = "longrun", verbose = TRUE))
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#> Call:
#> bvhar_horseshoe(y = etf_train, num_iter = 50, include_mean = FALSE, 
#>     minnesota = "longrun", verbose = TRUE)
#> 
#> BVHAR with Horseshoe Prior
#> Fitted by blocked sampling
#> Total number of iteration: 50
#> Number of burn-in: 25
#> ====================================================
#> 
#> # A draws_df: 25 iterations, 1 chains, and 103 variables
#>     phi[1]  phi[2]  phi[3]  phi[4]  phi[5]   phi[6]  phi[7]    phi[8]
#> 1    0.541   0.117  0.1022  0.0879   0.164  -0.0480  0.0431  -0.01197
#> 2    0.543   0.119  0.0983  0.0885   0.158  -0.0497  0.0587  -0.01417
#> 3    0.543   0.118  0.0992  0.0867   0.160  -0.0485  0.0502  -0.01051
#> 4    0.542   0.119  0.1020  0.0875   0.160  -0.0483  0.0427  -0.01106
#> 5    0.542   0.117  0.1058  0.0858   0.163  -0.0479  0.0427  -0.00992
#> 6    0.544   0.116  0.0949  0.0916   0.158  -0.0462  0.0488  -0.01830
#> 7    0.541   0.119  0.0966  0.0875   0.164  -0.0489  0.0497  -0.01049
#> 8    0.542   0.116  0.1020  0.0894   0.159  -0.0454  0.0485  -0.01446
#> 9    0.542   0.118  0.0954  0.0903   0.157  -0.0475  0.0556  -0.01525
#> 10   0.541   0.118  0.1012  0.0889   0.159  -0.0496  0.0491  -0.01307
#> # ... with 15 more draws, and 95 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot(fit_hs)

type = "dens" draws MCMC density plot.

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

Models with Stochastic Volatilities

SSVS

(fit_ssvs_sv <- bvhar_sv(etf_train, num_iter = 50, bayes_spec = set_ssvs(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_sv(y = etf_train, num_iter = 50, bayes_spec = set_ssvs(), 
#>     include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with Stochastic Volatility
#> Fitted by Gibbs sampling
#> Total number of iteration: 50
#> Number of burn-in: 25
#> ====================================================
#> 
#> Parameter Record:
#> # A draws_df: 25 iterations, 1 chains, and 354 variables
#>     phi[1]  phi[2]    phi[3]  phi[4]  phi[5]   phi[6]    phi[7]   phi[8]
#> 1    0.785  0.0793  -0.15126  0.2043   0.120   0.0907  -0.00864  -0.1397
#> 2    0.801  0.0824   0.04322  0.1067   0.125   0.0681  -0.06809  -0.0667
#> 3    0.770  0.0605  -0.00129  0.1077   0.125   0.0998  -0.11264  -0.0318
#> 4    0.739  0.0604  -0.03785  0.1134   0.176   0.0667  -0.08694  -0.0227
#> 5    0.789  0.0128  -0.01029  0.0443   0.174   0.1075  -0.02040   0.0418
#> 6    0.501  0.1494  -0.23357  0.3354   0.332  -0.0470   0.18223  -0.2315
#> 7    0.629  0.0438  -0.15867  0.2159   0.254   0.0901   0.15882  -0.0991
#> 8    0.522  0.1171  -0.26260  0.3145   0.361  -0.0327   0.12431  -0.2004
#> 9    0.493  0.1000  -0.29624  0.3133   0.271  -0.0120   0.21763  -0.0935
#> 10   0.461  0.1733  -0.42657  0.3467   0.108  -0.1280   0.30065   0.0165
#> # ... with 15 more draws, and 346 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot(fit_ssvs_sv)

Horseshoe

(fit_hs_sv <- bvhar_sv(etf_train, num_iter = 50, bayes_spec = set_horseshoe(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> bvhar_sv(y = etf_train, num_iter = 50, bayes_spec = set_horseshoe(), 
#>     include_mean = FALSE, minnesota = "longrun")
#> 
#> BVHAR with Stochastic Volatility
#> Fitted by Gibbs sampling
#> Total number of iteration: 50
#> Number of burn-in: 25
#> ====================================================
#> 
#> Parameter Record:
#> # A draws_df: 25 iterations, 1 chains, and 354 variables
#>     phi[1]  phi[2]     phi[3]  phi[4]     phi[5]   phi[6]   phi[7]   phi[8]
#> 1    0.433  0.0461  -6.93e-02   0.258   0.033938   0.0102   0.2708  0.00212
#> 2    0.431  0.0699   2.67e-02   0.263  -0.008923   0.0148   0.0480  0.04576
#> 3    0.490  0.0749  -2.72e-02   0.258  -0.060934   0.0119   0.1199  0.03617
#> 4    0.520  0.0476   1.77e-03   0.253   0.007058   0.0120   0.1069  0.04747
#> 5    0.516  0.0466   9.22e-05   0.214  -0.060572   0.0136   0.1859  0.12563
#> 6    0.527  0.0230   5.12e-02   0.219  -0.127866   0.0650  -0.0279  0.15157
#> 7    0.515  0.0455   1.52e-01   0.163   0.003174  -0.0635   0.2009  0.20966
#> 8    0.489  0.0640   1.70e-01   0.188  -0.050664  -0.0444   0.0661  0.17885
#> 9    0.498  0.0609   6.21e-02   0.232  -0.017296  -0.0285   0.2176  0.08531
#> 10   0.490  0.0705   2.49e-01   0.208   0.000344  -0.0650   0.0610  0.14936
#> # ... with 15 more draws, and 346 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}

autoplot(fit_hs_sv)

Shrinkage Priors

Stochastic Search Variable Selection (SSVS) Prior

Horseshoe Prior

Models with Stochastic Volatilities

SSVS

Horseshoe