submodel_test_statistics: Test Statistics for the Selection of Submodels of GVAR Model

In franzmohr/bgvars: Bayesian Inference of Global Vector Autoregressive and Gloal Vector Error Correction Models

Test Statistics for the Selection of Submodels of GVAR Model

Description

Calculates test statistics for the the selection of country-specific VARX or VECX models of a GVAR model.

Usage

submodel_test_statistics(object, ...)

Arguments

object	an object of class "bgvarest" or "bgvecest", usually, a result of a call to draw_posterior.gvarsubmodels or draw_posterior.gvecsubmodels, respectively.
...	further arguments passed to or from other methods.

Details

The log-likelihood for the calculation of the information criteria is obtained by

LL = \frac{1}{R} \sum_{i = 1}^{R} \left( \sum_{t = 1}^{T} -\frac{K^{dom}}{2} \ln 2\pi - \frac{1}{2} \ln |\Sigma_t^{(i)}| -\frac{1}{2} (u_t^{{(i)}\prime} (\Sigma_t^{(i)})^{-1} u_t^{(i)} \right)

, where u_t = y_t - \mu_t.

For VAR models the Akaike, Bayesian and Hannan–Quinn (HQ) information criteria are calculated as

AIC = 2 (K^{d}p^{d} + K^{f}p^{f} + Ms + N) - 2 LL

,

BIC = (K^{d}p^{d} + K^{f}p^{f} + Ms + N) ln(T) - 2 LL

and

HQ = 2 (K^{d}p^{d} + K^{f}p^{f} + Ms + N) ln(ln(T)) - 2 LL

, respectively, where K^{d} is the number of endogenous domestic variables, p^{d} the number of lags of endogenous domestic variables, K^{f} is the number of foreign variables, p^{f} the number of lags of foreign variables, M the number of global variables, s the number of lags of global variables, N the number of deterministic terms and T the number of observations.

Value

A list.

Examples

# Load data
data("gvar2019")

# Create regions
temp <- create_regions(country_data = gvar2019$country_data,
             weight_data = gvar2019$weight_data,
             region_weights = gvar2019$region_weights,
             regions = list(EA =  c("AT", "BE", "DE", "ES", "FI", "FR", "IT", "NL")),
             period = 3)

country_data <- temp$country_data
weight_data <- temp$weight_data
global_data = gvar2019$global_data

# Difference series to make them stationary
country_data <- diff_variables(country_data, variables = c("y", "Dp", "r"), multi = 100)
global_data <- diff_variables(global_data, multi = 100)

# Create time varying weights
weight_data <- create_weights(weight_data, period = 3, country_data = country_data)

# Generate specifications
model_specs <- create_specifications(
                 country_data = country_data,
                 global_data = global_data,
                 countries = c("US", "JP", "CA", "NO", "GB", "EA"), 
                 domestic = list(variables = c("y", "Dp", "r"), lags = 1),
                 foreign = list(variables = c("y", "Dp", "r"), lags = 1),
                 global = list(variables = c("poil"), lags = 1),
                 deterministic = list(const = TRUE, trend = FALSE, seasonal = FALSE),
                 iterations = 10,
                 burnin = 10)
# Note that the number of iterations and burnin draws should be much higher!
                                     
# Overwrite country-specific specifications
model_specs[["US"]][["domestic"]][["variables"]] <- c("y", "Dp", "r")
model_specs[["US"]][["foreign"]][["variables"]] <- c("y", "Dp")

# Create estimation objects
country_models <- create_models(country_data = country_data,
                                weight_data = weight_data,
                                global_data = global_data,
                                model_specs = model_specs)

# Add priors
models_with_priors <- add_priors(country_models,
                                 coef = list(v_i = 1 / 9, v_i_det = 1 / 10),
                                 sigma = list(df = 3, scale = .0001))

# Obtain posterior draws
object <- draw_posterior(models_with_priors)

# Obtain test statistics
tests <- submodel_test_statistics(object, ic = "BIC", select = "order")

franzmohr/bgvars documentation built on Sept. 2, 2023, 12:45 p.m.