gibbs_var: Gibbs sampler for vector autoregressive model.

In beyondWhittle: Bayesian Spectral Inference for Time Series

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)

beyondWhittle documentation built on June 22, 2024, 11:35 a.m.