gibbs_var {beyondWhittle}

Gibbs sampler for vector autoregressive model.

Description

Obtain samples of the posterior of a Bayesian VAR model of fixed order. An independent Normal-Inverse-Wishart prior is employed.

Usage

gibbs_var(
  data,
  ar.order,
  Ntotal,
  burnin,
  thin = 1,
  print_interval = 500,
  full_lik = F,
  beta.mu = rep(0, ar.order * ncol(data)^2),
  beta.Sigma = 10000 * diag(ar.order * ncol(data)^2),
  Sigma.S = 1e-04 * diag(ncol(data)),
  Sigma.nu = 1e-04
)

Arguments

data

numeric matrix; NA values are interpreted as missing values and treated as random

ar.order

order of the autoregressive model (integer >= 0)

Ntotal

total number of iterations to run the Markov chain

burnin

number of initial iterations to be discarded

thin

thinning number (postprocessing)

print_interval

Number of iterations, after which a status is printed to console

full_lik

logical; if TRUE, the full likelihood for all observations is used; if FALSE, the partial likelihood for the last n-p observations

beta.mu

prior mean of beta vector (normal)

beta.Sigma

prior covariance matrix of beta vector

Sigma.S

prior parameter for the innovation covariance matrix, symmetric positive definite matrix

Sigma.nu

prior parameter for the innovation covariance matrix, nonnegative real number

Details

See Section 2.2.3 in Koop and Korobilis (2010) or Section 6.2 in Meier (2018) for further details

Value

list containing the following fields:

beta

matrix containing traces of the VAR parameter vector beta

Sigma

trace of innovation covariance Sigma

psd.median, psd.mean

psd estimates: (pointwise, componentwise) posterior median and mean

psd.p05, psd.p95

pointwise credibility interval

psd.u05, psd.u95

uniform credibility interval, see (6.5) in Meier (2018)

lpost

trace of log posterior

References

G. Koop and D. Korobilis (2010) Bayesian Multivariate Time Series Methods for Empirical Macroeconomics Foundations and Trends in Econometrics <doi:10.1561/0800000013>

A. Meier (2018) A Matrix Gamma Process and Applications to Bayesian Analysis of Multivariate Time Series PhD thesis, OvGU Magdeburg <https://opendata.uni-halle.de//handle/1981185920/13470>

Examples

## Not run: 

##
## Example 1: Fit a VAR(p) model to SOI/Recruitment series:
##

# Use this variable to set the VAR model order
p <- 5

data <- cbind(as.numeric(astsa::soi-mean(astsa::soi)), 
              as.numeric(astsa::rec-mean(astsa::rec)) / 50)
data <- apply(data, 2, function(x) x-mean(x))

# If you run the example be aware that this may take several minutes
print("example may take some time to run")
mcmc <- gibbs_var(data=data, ar.order=p, Ntotal=10000, burnin=4000, thin=2)

# Plot spectral estimate, credible regions and periodogram on log-scale
plot(mcmc, log=T)



##
## Example 2: Fit a VAR(p) model to VMA(1) data
##

# Use this variable to set the VAR model order
p <- 5

n <- 256
ma <- rbind(c(-0.75, 0.5), c(0.5, 0.75))
Sigma <- rbind(c(1, 0.5), c(0.5, 1))
data <- sim_varma(model=list(ma=ma), n=n, d=2)
data <- apply(data, 2, function(x) x-mean(x))

# If you run the example be aware that this may take several minutes
print("example may take some time to run")
mcmc <- gibbs_var(data=data, ar.order=p, Ntotal=10000, burnin=4000, thin=2)

# Plot spectral estimate, credible regions and periodogram on log-scale
plot(mcmc, log=T)

## End(Not run)