etf <- etf_vix[1:55, 1:3]
# Split-------------------------------
h <- 5
etf_eval <- divide_ts(etf, h)
etf_train <- etf_eval$train
etf_test <- etf_eval$testModels 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
coef_spec- Minneosta prior
- BVAR:
set_bvar() - BVHAR:
set_bvhar()andset_weight_bvhar()
- BVAR:
- SSVS prior:
set_ssvs() - Horseshoe prior:
set_horseshoe() - NG prior:
set_ng() - DL prior:
set_dl()
- Minneosta prior
-
sv_spec: prior settings for SV,set_sv() -
intercept: prior for constant term,set_intercept()
set_sv()
#> Model Specification for SV with Cholesky Prior
#>
#> Parameters: Contemporaneous coefficients, State variance, Initial state
#> Prior: Cholesky
#> ========================================================
#> Setting for 'shape':
#> [1] rep(3, dim)
#>
#> Setting for 'scale':
#> [1] rep(0.01, dim)
#>
#> Setting for 'initial_mean':
#> [1] rep(1, dim)
#>
#> Setting for 'initial_prec':
#> [1] 0.1 * diag(dim)SSVS
(fit_ssvs <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, coef_spec = set_ssvs(), cov_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_ssvs(),
#> cov_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 177 variables
#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]
#> 1 0.0719 0.2090 0.10809 -0.980 -0.000526 0.3464 0.135 -0.0685
#> 2 -0.0233 -0.3991 -0.10453 0.414 0.075749 1.2320 -0.152 -0.1220
#> 3 0.0784 -0.1957 -0.04816 0.281 -0.027756 0.7372 0.145 -0.2823
#> 4 -0.1395 -0.1106 -0.06796 -0.135 -0.054614 0.8069 0.359 -0.0863
#> 5 -0.1870 -0.0175 0.03601 -0.102 -0.153686 0.7294 0.615 -0.3071
#> 6 0.4732 -0.0425 0.43854 -0.533 -0.045269 0.0988 1.189 -0.3845
#> 7 0.1115 -0.0724 0.07539 -0.499 0.042667 -0.0100 1.323 -0.2860
#> 8 -0.1291 -0.2984 0.00408 0.473 0.017545 -0.1782 1.586 -0.1215
#> 9 0.1372 -0.2387 -0.10112 0.204 -0.023939 0.6411 -0.158 0.0301
#> 10 0.0254 -0.2727 -0.05475 0.134 -0.003172 0.4632 0.218 0.0289
#> # ... with 10 more draws, and 169 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}Horseshoe
(fit_hs <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, coef_spec = set_horseshoe(), cov_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_horseshoe(),
#> cov_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 211 variables
#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]
#> 1 0.2305 -0.0596 -1.63e-03 0.1492 0.2418 -0.0172 0.445102 0.12523
#> 2 0.0807 -0.1439 8.46e-03 -0.0660 0.1012 -0.0764 0.760116 0.10467
#> 3 0.1378 -0.0970 -7.61e-03 -0.1445 0.4949 0.1310 0.114081 0.00523
#> 4 0.0641 -0.1928 5.79e-03 0.0624 0.2726 -0.0120 -0.327455 -0.04149
#> 5 -0.0749 -0.1716 -2.67e-03 -0.0628 0.1615 0.1056 0.060760 -0.06067
#> 6 -0.1128 -0.2914 8.26e-04 0.0410 0.2038 0.2036 0.017924 -0.03508
#> 7 0.1986 -0.1563 2.04e-03 0.0953 0.0288 0.4556 -0.029937 0.40808
#> 8 0.1010 -0.1697 -2.58e-04 0.0569 0.6293 0.6354 0.014622 -0.24877
#> 9 0.0250 -0.1645 9.27e-05 0.0751 0.2343 0.4192 0.007443 -0.08209
#> 10 0.0108 -0.1848 -1.46e-04 0.1697 0.5062 0.6513 -0.000994 -0.20476
#> # ... with 10 more draws, and 203 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}Normal-Gamma prior
(fit_ng <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, coef_spec = set_ng(), cov_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_ng(),
#> cov_spec = set_sv(), include_mean = FALSE, minnesota = "longrun")
#>
#> BVHAR with Stochastic Volatility
#> Fitted by Metropolis-within-Gibbs
#> Number of chains: 2
#> Total number of iteration: 20
#> Number of burn-in: 10
#> ====================================================
#>
#> Parameter Record:
#> # A draws_df: 10 iterations, 2 chains, and 184 variables
#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7] phi[8]
#> 1 0.25518 -0.9770 0.4259 0.417954 -0.1846 1.283 0.3877 -0.273345
#> 2 0.48881 -0.2540 -0.8135 0.656938 -0.0854 1.172 0.4056 0.000304
#> 3 -0.21958 0.7115 0.7059 -0.015675 0.4809 0.977 1.0520 -0.063890
#> 4 0.23791 -0.1875 0.1521 0.010566 0.2176 0.892 0.3509 -0.220596
#> 5 -0.11051 0.1282 0.2192 0.002291 0.2853 1.138 0.0922 -0.186967
#> 6 -0.24014 -0.1462 0.1873 -0.002420 0.0432 0.711 -0.2923 -0.056603
#> 7 0.12877 -0.0630 -0.0936 -0.006839 0.4895 1.106 0.8267 0.109545
#> 8 0.00938 -0.3370 0.1838 0.021547 -0.2261 1.386 0.3885 0.111162
#> 9 0.00284 -0.0438 0.0134 0.004785 0.9719 1.899 -0.0484 -0.078218
#> 10 -0.01474 -0.0781 -0.0557 0.000692 0.8656 1.593 -0.4511 0.007074
#> # ... with 10 more draws, and 176 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}Dirichlet-Laplace prior
(fit_dl <- vhar_bayes(etf_train, num_chains = 2, num_iter = 20, coef_spec = set_dl(), cov_spec = set_sv(), include_mean = FALSE, minnesota = "longrun"))
#> Call:
#> vhar_bayes(y = etf_train, num_chains = 2, num_iter = 20, coef_spec = set_dl(),
#> cov_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 178 variables
#> phi[1] phi[2] phi[3] phi[4] phi[5] phi[6] phi[7]
#> 1 0.01572 2.43e-02 0.09985 0.452805 0.00257 0.966 -0.385
#> 2 0.01141 1.05e-02 0.09363 0.376326 0.00332 0.762 -0.857
#> 3 -0.02085 -4.18e-03 0.32863 0.420273 -0.01554 0.796 -0.569
#> 4 -0.05024 1.34e-03 0.45740 0.001272 -0.02070 0.867 -1.440
#> 5 0.02476 -6.36e-04 0.49315 0.001427 0.01904 0.939 -1.162
#> 6 0.02065 -4.09e-04 0.06321 0.000834 0.53316 0.899 -1.165
#> 7 -0.02309 -1.71e-03 -0.00409 -0.001295 0.77605 0.843 -1.231
#> 8 -0.00636 -1.91e-04 -0.01217 -0.000551 0.62815 0.862 -1.257
#> 9 -0.02534 2.71e-05 0.00684 0.000970 0.55055 0.871 -0.925
#> 10 -0.02044 -7.04e-05 -0.01042 -0.006080 0.71595 0.871 -0.738
#> phi[8]
#> 1 -0.00553
#> 2 0.00288
#> 3 0.02929
#> 4 -0.39449
#> 5 -0.18117
#> 6 -0.20311
#> 7 -0.21344
#> 8 -0.34973
#> 9 -0.09570
#> 10 -0.00752
#> # ... with 10 more draws, and 170 more variables
#> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}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")