as.mbsts {CausalMBSTS}

Definition and estimation of a Multivariate Bayesian Structural Time Series model (MBSTS)

Description

The function creates a multivariate Bayesian structural time series model. It then estimates the model, samples from the joint posterior distribution of its parameters, and outputs an object of class mbsts.

Usage

as.mbsts(
  y,
  components,
  seas.period = NULL,
  cycle.period = NULL,
  X = NULL,
  H = NULL,
  nu0.r = NULL,
  s0.r = 0.01 * var(y, na.rm = TRUE),
  nu0.eps = NULL,
  s0.eps = 0.01 * var(y, na.rm = TRUE),
  niter,
  burn,
  ping = NULL
)

Arguments

y

t x d data.frame (or matrix) of observations, where d is the number of time series in the multivariate model.

components

Character vector specifying the components of the multivariate structural time series model. Possible values are c("trend", "slope", "seasonal", "cycle").

seas.period

Length of the seasonal pattern, if present.

cycle.period

Length of the cycle pattern, if present.

X

Optional t x N data frame (or matrix) of N 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 = c*diag((X'X)^(-1)) or H = c*I. 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 element of Sigma.r, a vector of errors for state r. Set by default to d + 2 (must be greater than d - 1).

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 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.

Value

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))
mbsts.1 <- as.mbsts(y = y, components = c("trend", "seasonal"), seas.period = 7,
                    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)
mbsts.2 <- as.mbsts(y = y, components = c("trend", "seasonal"), , seas.period = 7,
                    X = X, s0.r = diag(2), s0.eps = diag(2), niter = 100, burn = 10)