R6 Class Representing PriorBVAR

The class PriorBVAR presents a prior specification for the BVAR model.

#' The Model. All the BVAR models in this package are specified by two equations, including the reduced form equation: $$Y = AX + E$$ where $Y$ is an NxT matrix of dependent variables, $X$ is a KxT matrix of explanatory variables, $E$ is an NxT matrix of reduced form error terms, and $A$ is an NxK matrix of autoregressive slope coefficients and parameters on deterministic terms in $X$.

This package assumes that the error matrix follows a matrix normal distribution: $$E \mid X \sim \mathcal{MN}_{N \times T}(\mathbf{0}, \mathbf{\Sigma}, \mathbf{\Omega})$$ where $\Sigma$ is the NxN covariance matrix of the error term at time $t$, and $\Omega$ is a TxT diagonal matrix.

The diagonal elements of $\Omega$ determine the specification of the error term covariance structure. Specifically, the error term at time $t$ follows the multivariate normal distribution $$e_t \sim \mathcal{N}_N(\mathbf{0}, \sigma_t^2\lambda_t \mathbf{\Sigma})$$ where the scalar processes $\sigma_t^2$ and $\lambda_t$ determine the diagonal elements of $\Omega$. The process $\sigma_t^2$ specifies conditional variance and includes three options:

$\sigma_t^2 = 1$: homoskedastic error term
$\sigma_t^2$: estimated and following non-centred stochastic volatility
$\sigma_t^2$: estimated and following centred stochastic volatility

The process $\lambda_t$ specifies the conditional distribution of the error term and includes two options:

$\lambda_t = 1$: Gaussian error term specification
$\lambda_t$: estimated and following a priori an inverse gamma 2 distribution $\mathcal{IG}2(\nu - 2, \nu)$, where $\nu > 2$ is a degrees of freedom parameter

Prior distributions. The autoregressive matrix $A$ is assigned matrix-variate normal distribution: $$ \mathbf{A} \mid \underline{\mathbf{A}}, \mathbf{V}, \boldsymbol{\Sigma} \sim \mathcal{MN}_{N \times K}(\underline{\mathbf{A}}, \boldsymbol{\Sigma}, \mathbf{V}) $$ with the mean matrix $\underline{\mathbf{A}}$, and covariance matrices $\boldsymbol{\Sigma}_{N\times N}$ and $\mathbf{V}_{K\times K}$ defining the row- and column-covariance structures.

This is complemented by the inverse Wishart prior for the error term covariance $\boldsymbol{\Sigma}$: $$ \boldsymbol{\Sigma} \mid \underline{\mathbf{S}}, \underline{\nu} \sim \mathcal{IW}(\underline{\mathbf{S}}, \underline{\nu}) $$ with the scale matrix $\underline{\mathbf{S}}$ and degrees of freedom $\underline{\nu}$.

Public fields

A: a real-valued NxK matrix, the mean matrix $A_0$ of the matrix-variate normal prior distribution for the parameter matrix $A$.
S: a NxN positive definite scale matrix $S_0$ of the Inverse Wishart prior distribution for the error term covariance matrix $\Sigma$.
nu: a positive scalar, shape parameter $\nu_0$ of the Inverse Wishart prior distribution for the error term covariance matrix $\Sigma$.
Psi: a KxK scale matrix $\Psi_0$ of the matrix generalized inverse Gaussian distribution for the equation-specific prior covariance $V$
Gamma: a KxK scale matrix $\Gamma_0$ of the matrix generalized inverse Gaussian distribution for the equation-specific prior covariance $V$
lambda: a positive scalar shape parameter $\lambda_0$ of the matrix generalized inverse Gaussian distribution for the equation-specific prior covariance $V$
sv_a: a positive scalar, the shape parameter of the gamma prior in the hierarchical prior for the common stochastic volatility.
sv_s: a positive scalar, the scale parameter of the gamma prior in the hierarchical prior for the common stochastic volatility.

Methods

Method `new()`

Create a new prior specification PriorBVAR.

Usage

specify_prior_bvar$new(
  N,
  p,
  d = 0,
  stationary = rep(FALSE, N),
  is_homoskedastic = TRUE
)

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the VAR model.
d: a positive integer - the number of exogenous variables in the model.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.
is_homoskedastic: a logical scalar - if TRUE the model assumes homoskedastic errors, otherwise it assumes stochastic volatility.

Returns

A new prior specification PriorBVAR.

Examples

# a prior for 3-variable example with one lag and stationary data
prior = specify_prior_bvar$new(N = 3, p = 1, stationary = rep(TRUE, 3))
prior$A # show autoregressive prior mean

Method `get_prior()`

Returns the elements of the prior specification PriorBVAR as a list.

Usage

specify_prior_bvar$get_prior()

Examples

# a prior for 3-variable example with four lags
prior = specify_prior_bvar$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_prior_bvar$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

prior = specify_prior_bvar$new(N = 3, p = 1)  # a prior for 3-variable example with one lag
prior$A                                        # show autoregressive prior mean
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    0    0    0
#> [2,]    0    1    0    0
#> [3,]    0    0    1    0


## ------------------------------------------------
## Method `specify_prior_bvar$new`
## ------------------------------------------------

# a prior for 3-variable example with one lag and stationary data
prior = specify_prior_bvar$new(N = 3, p = 1, stationary = rep(TRUE, 3))
prior$A # show autoregressive prior mean
#>      [,1] [,2] [,3] [,4]
#> [1,]    0    0    0    0
#> [2,]    0    0    0    0
#> [3,]    0    0    0    0


## ------------------------------------------------
## Method `specify_prior_bvar$get_prior`
## ------------------------------------------------

# a prior for 3-variable example with four lags
prior = specify_prior_bvar$new(N = 3, p = 4)
prior$get_prior() # show the prior as list
#> $A
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#> [2,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#> [3,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#> 
#> $S
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1
#> 
#> $nu
#> [1] 6
#> 
#> $Psi
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#>  [2,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#>  [3,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#>  [4,]    0    0    0    1    0    0    0    0    0     0     0     0     0
#>  [5,]    0    0    0    0    1    0    0    0    0     0     0     0     0
#>  [6,]    0    0    0    0    0    1    0    0    0     0     0     0     0
#>  [7,]    0    0    0    0    0    0    1    0    0     0     0     0     0
#>  [8,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#>  [9,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [10,]    0    0    0    0    0    0    0    0    0     1     0     0     0
#> [11,]    0    0    0    0    0    0    0    0    0     0     1     0     0
#> [12,]    0    0    0    0    0    0    0    0    0     0     0     1     0
#> [13,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#> 
#> $Gamma
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,]    1    0    0    0    0    0    0    0    0     0     0     0     0
#>  [2,]    0    1    0    0    0    0    0    0    0     0     0     0     0
#>  [3,]    0    0    1    0    0    0    0    0    0     0     0     0     0
#>  [4,]    0    0    0    1    0    0    0    0    0     0     0     0     0
#>  [5,]    0    0    0    0    1    0    0    0    0     0     0     0     0
#>  [6,]    0    0    0    0    0    1    0    0    0     0     0     0     0
#>  [7,]    0    0    0    0    0    0    1    0    0     0     0     0     0
#>  [8,]    0    0    0    0    0    0    0    1    0     0     0     0     0
#>  [9,]    0    0    0    0    0    0    0    0    1     0     0     0     0
#> [10,]    0    0    0    0    0    0    0    0    0     1     0     0     0
#> [11,]    0    0    0    0    0    0    0    0    0     0     1     0     0
#> [12,]    0    0    0    0    0    0    0    0    0     0     0     1     0
#> [13,]    0    0    0    0    0    0    0    0    0     0     0     0     1
#> 
#> $lambda
#> [1] 4
#> 
#> $sv_a
#> [1] NA
#> 
#> $sv_s
#> [1] NA
#>

Public fields

Methods

Public methods

Method new()

Usage

Arguments

Returns

Examples

Method get_prior()

Usage

Examples

Method clone()

Usage

Arguments

Examples

R6 Class Representing `PriorBVAR`

Method `new()`

Method `get_prior()`

Method `clone()`