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,
  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)
verbose: Print the progress bar in the console. By default, FALSE.
num_thread: Number of threads
x: Any 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      1.5366349054 0.0016615036 -1.506726e-02
#> OVXCLS_day     -0.0026524127 0.9359349918 -5.708013e-03
#> VXFXICLS_day   -0.0146310590 0.0024995591  1.537258e+00
#> GVZCLS_week    -0.0092233616 0.0004157423 -3.630363e-03
#> OVXCLS_week    -0.0005597116 0.0013866635 -1.384420e-03
#> VXFXICLS_week  -0.0034344491 0.0007286726 -9.230511e-03
#> GVZCLS_month   -0.0033022777 0.0002368569 -1.336567e-03
#> OVXCLS_month   -0.0001072453 0.0006003371 -5.396754e-04
#> VXFXICLS_month -0.0013234128 0.0003103822 -3.081001e-03
#> const          -8.9686314530 1.6366720182 -1.242785e+01
head(residuals(fit))
#>            [,1]      [,2]      [,3]
#> [1,] -0.8194821 0.1336131 -3.049195
#> [2,] -1.8555011 0.3284684 -3.173116
#> [3,] -1.1557180 0.6285560  1.092094
#> [4,] -1.3084869 0.7160126 -4.866712
#> [5,] -0.1447166 0.6198937 -3.215935
#> [6,] -0.3712924 1.5118750 -2.461061
head(fitted(fit))
#>        GVZCLS   OVXCLS VXFXICLS
#> [1,] 21.50948 32.18639 32.50920
#> [2,] 21.88550 32.10153 31.84312
#> [3,] 20.88572 32.20144 30.63791
#> [4,] 20.37849 32.58399 35.33671
#> [5,] 19.38472 33.02011 33.40593
#> [6,] 19.65129 33.33813 32.97106