mtar {mtarm}

Bayesian estimation of a multivariate threshold autoregressive (TAR) model.

Description

This function uses Gibbs sampling to generate a sample from the posterior distribution of the parameters of a multivariate TAR model when the noise process follows Gaussian, Student-t, Slash, Symmetric Hyperbolic, Contaminated normal, or Laplace distribution.

Usage

mtar(
  formula,
  data,
  subset,
  Intercept = TRUE,
  ars,
  row.names,
  dist = "Gaussian",
  prior = list(),
  n.sim = 500,
  n.burnin = 100,
  n.thin = 1,
  log = FALSE,
  ...
)

Arguments

formula

a three-part expression of type Formula describing the TAR model to be fitted to the data. In the first part, the variables in the multivariate output series are listed; in the second part, the threshold series is specified, and in the third part, the variables in the multivariate exogenous series are specified.

data

an (optional) data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which mtar is called.

subset

an (optional) vector specifying a subset of observations to be used in the fitting process.

Intercept

an (optional) logical variable. If TRUE, then the model includes an intercept.

ars

a list composed of three objects, namely: p, q and d, each of which corresponds to a vector of non-negative integers with as many elements as there are regimes in the TAR model.

row.names

an (optional) vector that allows the user to name the time point to which each row in the data set corresponds.

dist

an (optional) character string that allows the user to specify the multivariate distribution to be used to describe the behavior of the noise process. The available options are: Gaussian ("Gaussian"), Student-t ("Student-t"), Slash ("Slash"), Symmetric Hyperbolic ("Hyperbolic"), Laplace ("Laplace"), and contaminated normal ("Contaminated normal"). As default, dist is set to "Gaussian".

prior

an (optional) list that allows the user to specify the values of the hyperparameters, that is, allows to specify the values of the parameters of the prior distributions.

n.sim

an (optional) positive integer specifying the required number of iterations for the simulation after the burn-in period. As default, n.sim is set to 500.

n.burnin

an (optional) positive integer specifying the required number of burn-in iterations for the simulation. As default, n.burnin is set to 100.

n.thin

an (optional) positive integer specifying the required thinning interval for the simulation. As default, n.thin is set to 1.

log

an (optional) logical variable. If TRUE, then the behaviour of the output series is described using the exponentiated version of dist.

...

further arguments passed to or from other methods.

Value

an object of class mtar in which the main results of the model fitted to the data are stored, i.e., a list with components including

chains	list with several arrays, which store the values of each model parameter in each iteration of the simulation,
n.sim	number of iterations of the simulation after the burn-in period,
n.burnin	number of burn-in iterations in the simulation,
n.thin	thinning interval in the simulation,
regim	number of regimes,
ars	list composed of three objects, namely: p, q and d, each of which corresponds to a vector of non-negative integers with as many elements as there are regimes in the TAR model,
dist	name of the multivariate distribution used to describe the behavior of the noise process,
threshold.series	vector with the values of the threshold series,
response.series	matrix with the values of the output series,
covariable.series	matrix with the values of the exogenous series,
Intercept	If TRUE, then the model included an intercept term,
formula	the formula,
call	the original function call.

References

Nieto, F.H. (2005) Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data. Communications in Statistics - Theory and Methods, 34, 905-930.

Romero, L.V. and Calderon, S.A. (2021) Bayesian estimation of a multivariate TAR model when the noise process follows a Student-t distribution. Communications in Statistics - Theory and Methods, 50, 2508-2530.

Calderon, S.A. and Nieto, F.H. (2017) Bayesian analysis of multivariate threshold autoregressive models with missing data. Communications in Statistics - Theory and Methods, 46, 296-318.

See Also

DIC, WAIC

Examples

###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar(~ COLCAP + BOVESPA | SP500, row.names=Date, dist="Slash",
             data=returns, ars=list(p=c(1,1,2)), n.burnin=100, n.sim=3000)
summary(fit1)

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar(~ Bedon + LaPlata | Rainfall, row.names=Date, dist="Laplace",
             data=riverflows, ars=list(p=c(5,5,5)), n.burnin=100, n.sim=3000)
summary(fit2)