Fitting Bayesian VHAR of Minnesota Prior

This function fits BVHAR with Minnesota prior.

Usage

bvhar_minnesota(
  y,
  har = c(5, 22),
  num_chains = 1,
  num_iter = 1000,
  num_burn = floor(num_iter/2),
  thinning = 1,
  bayes_spec = set_bvhar(),
  scale_variance = 0.05,
  include_mean = TRUE,
  parallel = list(),
  verbose = FALSE,
  num_thread = 1
)

# S3 method for class 'bvharmn'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

# S3 method for class 'bvharhm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

# S3 method for class 'bvharmn'
logLik(object, ...)

# S3 method for class 'bvharmn'
AIC(object, ...)

# S3 method for class 'bvharmn'
BIC(object, ...)

is.bvharmn(x)

# S3 method for class 'bvharmn'
knit_print(x, ...)

# S3 method for class 'bvharhm'
knit_print(x, ...)

Arguments

y: Time series data of which columns indicate the variables
har: Numeric vector for weekly and monthly order. By default, c(5, 22).
num_chains: Number of MCMC chains
num_iter: MCMC iteration number
num_burn: Number of burn-in (warm-up). Half of the iteration is the default choice.
thinning: Thinning every thinning-th iteration
bayes_spec: A BVHAR model specification by set_bvhar() (default) or set_weight_bvhar().
scale_variance: Proposal distribution scaling constant to adjust an acceptance rate
include_mean: Add constant term (Default: TRUE) or not (FALSE)
parallel: List the same argument of optimParallel::optimParallel(). By default, this is empty, and the function does not execute parallel computation.
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: bvharhm object
digits: digit option to print
...: not used
object: A bvharmn object

Value

bvhar_minnesota() returns an object bvharmn class. It is a list with the following components:

coefficients: Posterior Mean
fitted.values: Fitted values
residuals: Residuals
mn_mean: Posterior mean matrix of Matrix Normal distribution
mn_prec: Posterior precision matrix of Matrix Normal distribution
iw_scale: Posterior scale matrix of posterior inverse-wishart distribution
iw_shape: Posterior shape of inverse-Wishart distribution ($\nu_0$ - obs + 2). $\nu_0$: nrow(Dummy observation) - k
df: Numer of Coefficients: 3m + 1 or 3m
m: Dimension of the time series
obs: Sample size used when training = totobs - 22
prior_mean: Prior mean matrix of Matrix Normal distribution: $M_0$
prior_precision: Prior precision matrix of Matrix Normal distribution: $\Omega_0^{-1}$
prior_scale: Prior scale matrix of inverse-Wishart distribution: $\Psi_0$
prior_shape: Prior shape of inverse-Wishart distribution: $\nu_0$
y0: $Y_0$
design: $X_0$
p: 3, this element exists to run the other functions
week: Order for weekly term
month: Order for monthly term
totobs: Total number of the observation
type: include constant term (const) or not (none)
HARtrans: VHAR linear transformation matrix: $C_{HAR}$
y: Raw input (matrix)
call: Matched call
process: Process string in the bayes_spec: BVHAR_MN_VAR (BVHAR-S) or BVHAR_MN_VHAR (BVHAR-L)
spec: Model specification (bvharspec)

It is also normaliw and bvharmod class.

Details

Apply Minnesota prior to Vector HAR: $\Phi$ (VHAR matrices) and $\Sigma_e$ (residual covariance).

$$\Phi \mid \Sigma_e \sim MN(M_0, \Omega_0, \Sigma_e)$$ $$\Sigma_e \sim IW(\Psi_0, \nu_0)$$ (MN: matrix normal, IW: inverse-wishart)

There are two types of Minnesota priors for BVHAR:

VAR-type Minnesota prior specified by set_bvhar(), so-called BVHAR-S model.
VHAR-type Minnesota prior specified by set_weight_bvhar(), so-called BVHAR-L model.

References

Kim, Y. G., and Baek, C. (2024). Bayesian vector heterogeneous autoregressive modeling. Journal of Statistical Computation and Simulation, 94(6), 1139-1157.

Examples

# Perform the function using etf_vix dataset
fit <- bvhar_minnesota(y = etf_vix[,1:3])
class(fit)
#> [1] "bvharmn"  "bvharmod" "normaliw"

# Extract coef, fitted values, and residuals
coef(fit)
#>                       GVZCLS        OVXCLS      VXFXICLS
#> GVZCLS_day      9.563078e-01  0.0049571622  0.0023012975
#> OVXCLS_day     -1.124095e-03  0.9934581488  0.0021059646
#> VXFXICLS_day   -3.655575e-04 -0.0196286064  0.9707085757
#> GVZCLS_week     7.114698e-04  0.0003115497 -0.0029533997
#> OVXCLS_week    -1.272095e-03 -0.0007333494 -0.0010949289
#> VXFXICLS_week   2.842160e-03  0.0074516208 -0.0054726494
#> GVZCLS_month    9.807968e-03  0.0035140103  0.0030645736
#> OVXCLS_month   -8.954785e-05  0.0008878183  0.0008366598
#> VXFXICLS_month  1.183747e-03  0.0012979345 -0.0008406757
#> const           5.747434e-01  0.2878285856  0.7849725826
head(residuals(fit))
#>             [,1]        [,2]        [,3]
#> [1,]  0.31184618 -0.01743843 -0.26993926
#> [2,] -0.57825789  0.17050304 -0.64147554
#> [3,] -0.24663283  0.44836077  3.18688370
#> [4,] -0.61879508  0.57710447 -1.03884178
#> [5,]  0.18365992  0.42795339 -0.09427081
#> [6,]  0.06251278  1.29400222  0.49667649
head(fitted(fit))
#>        GVZCLS   OVXCLS VXFXICLS
#> [1,] 20.37815 32.33744 29.72994
#> [2,] 20.60826 32.25950 29.31148
#> [3,] 19.97663 32.38164 28.54312
#> [4,] 19.68880 32.72290 31.50884
#> [5,] 19.05634 33.21205 30.28427
#> [6,] 19.21749 33.55600 30.01332