mcmc function

MCMC samples for a given MBSTS model

Use MCMC to sample from the joint posterior of model parameters in an mbsts model.

mcmc(
  Smodel,
  X = NULL,
  H = NULL,
  nu0.r = NULL,
  s0.r,
  nu0.eps = NULL,
  s0.eps,
  niter,
  burn,
  ping = NULL
)

Arguments

• Smodel: A multivariate state space model of class SSModel.
• X: t x N optional matrix of predictors.
• H: P x P variance-covariance matrix of the regression coefficients. Set by default to H = c(X'X)^(-1) which is akin to the Zellner's g-prior. The value of the scaling factor is set to c = 1. Alternative priors could be H = cdiag((X'X)^(-1)) or H = cI. See also Smith & Kohn, 1995 that suggest setting c in the range [10,1000].
• nu0.r: Degrees of freedom of the Inverse-Wishart prior for each Sigma.r. Set by default to n0.r = d + 2, where d is the number of time series in the multivariate model.
• s0.r: Scale matrix of the Inverse-Wishart prior for each Sigma.r, a vector of errors for state r. Must be a (d x d) positive definite. Default set to the variance-covariance matrix of y multiplied by a scaling factor of 0.01.
• nu0.eps: Degrees of freedom of the Inverse-Wishart prior for Sigma.eps, a vector of observation errors for each time series. Set by default to d + 2 (must be greater than d - 1).
• s0.eps: Scale matrix of the Inverse-Wishart prior for Sigma.eps, a vector of observation errors for each time series. Must be a (d x d) positive definite. Default set to the variance-covariance matrix of y multiplied by a scaling factor of 0.01.
• niter: Number of MCMC iterations.
• burn: Desired burn-in, set by default to 0.1 * niter.
• ping: A status message is printed every ping iteration. Default set to 0.1 * niter. Set to 0 to not track the status.

Returns

An object of class 'mbsts' which is a list with the following components:

• eta.samples: (niter- burn) draws from the distribution of eta_r.
• eps.samples: (niter- burn) draws from the distribution of eps.
• states.samples: (niter- burn) draws from p(alpha_t | Y_1:T).
• Sigma.r: (niter- burn) draws from the posterior distribution of Sigma.r.
• Sigma.eps: (niter- burn) draws from the posterior distribution of Sigma.eps.
• Z.beta: (niter- burn) x P matrix of the models selected at each iteration (if a matrix of predictors is provided).
• beta: P x d x (niter- burn) ) array of the draws from the posterior distribution of the regression coefficient matrix (if a matrix of predictors is provided).
• X: Predictor matrix (if provided).
• y: Matrix of observations.
• Z: (d x m) selection matrix of the observation equation.
• Tt: (m x m) matrix of the state equation.
• R: (m x r) matrix selecting the state disturbances.
• niter: Number of mcmc iterations.
• burn: Burn-in.

Examples

## Example 1 : local level + seasonal (d = 3)
y <- cbind(seq(0.5,100,by=0.5)*0.1 + rnorm(200),
           seq(100.25,150,by=0.25)*0.05 + rnorm(200),
           rnorm(200, 5,1))
model.1 <- model(y = y, components = c("trend", "seasonal"), seas.period = 7)
mcmc.1 <- mcmc(model.1, s0.r = diag(3), s0.eps = diag(3), niter = 50, burn = 5)

## Example 2 : local level + seasonal + covariates (d = 2)
y <- cbind(rnorm(100), rnorm(100, 2, 3))
X <- cbind(rnorm(100, 0.5, 1) + 5, rnorm(100, 0.2, 2) - 2)
model.2 <- model(y = y, components = c("trend", "seasonal"), seas.period = 7)
mcmc.2 <- mcmc(model.2, X = X, s0.r = diag(2), s0.eps = diag(2), niter = 100, burn = 10)