Bayesian Estimation of Multivariate TAR Models

This function is a wrapper that applies mtar() over a grid of model specifications defined by all combinations of the noise distribution (dist), the number of regimes (from nregim.min to nregim.max), the autoregressive order within each regime (from p.min to p.max), the maximum lag of the exogenous series within each regime (from q.min to q.max), and the maximum lag of the threshold series within each regime (from d.min to d.max). In all calls to mtar(), the same set of time points is used for model fitting. This is achieved by appropriately adjusting the subset argument of mtar() for each model specification, thereby ensuring comparability across models.

Usage

mtar_grid(
  formula,
  data,
  subset,
  Intercept = TRUE,
  trend = c("none", "linear", "quadratic"),
  nseason = NULL,
  nregim.min = 1,
  nregim.max = NULL,
  p.min = 1,
  p.max = NULL,
  q.min = 0,
  q.max = 0,
  d.min = 0,
  d.max = 0,
  row.names,
  dist = "Gaussian",
  prior = list(),
  n.sim = 500,
  n.burnin = 100,
  n.thin = 1,
  ssvs = FALSE,
  setar = NULL,
  plan_strategy = c("multisession", "sequential"),
  progress = TRUE
)

Arguments

formula: A three-part expression of class Formula describing the TAR model to be fitted. The first part specifies the variables in the multivariate output series, the second part defines the threshold series, and the third part specifies the variables in the multivariate exogenous series.
data: 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_grid() is called.
subset: An optional vector specifying a subset of observations to be used in the fitting process.
Intercept: An optional logical indicating whether an intercept should be included within each regime.
trend: An optional character string specifying the degree of deterministic time trend to be included in each regime. Available options are "linear", "quadratic", and "none". By default, trend is set to "none".
nseason: An optional integer, greater than or equal to 2, specifying the number of seasonal periods. When provided, nseason - 1 seasonal dummy variables are added to the regressors within each regime. By default, nseason is set to NULL, thereby indicating that the TAR model has no seasonal effects.
nregim.min: An optional integer specifying the minimum number of regimes. By default, nregim.min is set to 1.
nregim.max: An integer specifying the maximum number of regimes.
p.min: An optional integer specifying the minimum autoregressive order within each regime. By default, p.min is set to 1.
p.max: An integer specifying the maximum autoregressive order within each regime.
q.min: An optional integer specifying the minimum value of the maximum lag of the exogenous series within each regime. By default, q.min is set to 0.
q.max: An optional integer specifying the maximum value of the maximum lag of the exogenous series within each regime. By default, q.max is set to 0.
d.min: An optional integer specifying the minimum value of the maximum lag of the threshold series within each regime. By default, d.min is set to 0.
d.max: An optional integer specifying the maximum value of the maximum lag of the threshold series within each regime. By default, d.max is set to 0.
row.names: An optional variable in data labelling the time points corresponding to each row of the data set.
dist: A character vector specifying the multivariate distributions used to model the noise process. Available options are "Gaussian", "Student-t", "Slash", "Hyperbolic", "Laplace", "Contaminated normal", "Skew-normal", and "Skew-Student-t". By default, dist is set to "Gaussian".
prior: An optional list specifying the hyperparameter values that define the prior distribution. This list can be validated using the priors() function. By default, prior is set to an empty list, thereby indicating that the hyperparameter values should be set so that a non-informative prior distribution is obtained.
n.sim: An optional positive integer specifying the number of simulation iterations after the burn-in period. By default, n.sim is set to 500.
n.burnin: An optional positive integer specifying the number of burn-in iterations. By default, n.burnin is set to 100.
n.thin: An optional positive integer specifying the thinning interval. By default, n.thin is set to 1.
ssvs: An optional logical indicating whether the Stochastic Search Variable Selection (SSVS) procedure should be applied to identify relevant lags of the output, exogenous, and threshold series. By default, ssvs is set to FALSE.
setar: An optional positive integer indicating the component of the output series used as the threshold variable. By default, setar is set to NULL, indicating that the fitted model is not a SETAR model.
plan_strategy: An optional character string specifying the execution strategy for parallel computation. Available options are "sequential" and "multisession". By default, plan_strategy is set to "sequential".
progress: An optional logical indicating whether a progress bar should be displayed during execution. By default, progress is set to TRUE.

Value

A list whose elements are objects of class mtar, each corresponding to a distinct model specification considered in the grid.

Examples

# \donttest{
###### Example 1: Returns of the closing prices of three financial indexes
data(returns)
fit1 <- mtar_grid(~ COLCAP + BOVESPA | SP500, data=returns, row.names=Date,
                  subset={Date<="2015-12-07"}, dist=c("Gaussian","Student-t",
                  "Slash","Laplace"), nregim.min=2, nregim.max=3, p.min=2,
                  p.max=2, n.burnin=100, n.sim=200, n.thin=2,
                  plan_strategy="multisession")
summary(fit1)
#>               Length Class Mode
#> Gaussian.2.2  24     mtar  list
#> Gaussian.3.2  24     mtar  list
#> Laplace.2.2   24     mtar  list
#> Laplace.3.2   24     mtar  list
#> Slash.2.2     24     mtar  list
#> Slash.3.2     24     mtar  list
#> Student-t.2.2 24     mtar  list
#> Student-t.3.2 24     mtar  list

###### Example 2: Rainfall and two river flows in Colombia
data(riverflows)
fit2 <- mtar_grid(~ Bedon + LaPlata | Rainfall, data=riverflows,
                  row.names=Date, subset={Date<="2009-02-13"},dist="Laplace",
                  nregim.min=2, nregim.max=3, p.min=1, p.max=3,n.burnin=100,
                  n.sim=200, n.thin=2, plan_strategy="multisession")
fit2
#> 
#> 
#> Sample size          :1137 time points (2006-01-04 to 2009-02-13)
#> 
#> Output Series        :Bedon    |    LaPlata
#> 
#> Threshold Series     :Rainfall with a estimated delay equal to 0
#> 
#> Error Distribution   :Laplace
#> 
#> Number of regimes    :2 to 3
#> 
#> Deterministics       :Intercept  
#> 
#> Autoregressive orders:1 to 3

###### Example 3: Temperature, precipitation, and two river flows in Iceland
data(iceland.rf)
fit3 <- mtar_grid(~ Jokulsa + Vatnsdalsa | Temperature | Precipitation,
                  data=iceland.rf,subset={Date<="1974-11-06"},row.names=Date,
                  dist=c("Slash","Student-t"), nregim.min=1, nregim.max=2,
                  p.min=15, p.max=15, q.min=4, q.max=4, d.min=2, d.max=2,
                  n.burnin=100, n.sim=200, n.thin=2,
                  plan_strategy="multisession")
fit3
#> 
#> 
#> Sample size          :1026 time points (1972-01-16 to 1974-11-06)
#> 
#> Output Series        :Jokulsa    |    Vatnsdalsa
#> 
#> Exogenous Series (ES):Precipitation
#> 
#> Error Distribution   :Slash
#> 
#> Number of regimes    :1 to 2
#> 
#> Deterministics       :Intercept  
#> 
#> Autoregressive orders:15 to 15
#> 
#> Maximum lags for ES  :4 to 4

###### Example 4: U.S. stock returns
data(US.returns)
fit4 <- mtar_grid(~ CCR | dVIX, data=US.returns, subset={Date<="2025-11-28"},
                  row.names=Date, dist=c("Laplace","Student-t","Slash"),
                  nregim.min=2, nregim.max=2, p.min=3, p.max=3, d.min=3,
                  d.max=3, n.burnin=100, n.sim=200, n.thin=2,
                  plan_strategy="multisession")
fit4
#> 
#> 
#> Sample size          :5317 time points (2005-01-10 to 2025-11-28)
#> 
#> Output Series        :CCR
#> 
#> Threshold Series (TS):dVIX with a estimated delay equal to 0
#> 
#> Error Distribution   :Laplace
#> 
#> Number of regimes    :2 to 2
#> 
#> Deterministics       :Intercept  
#> 
#> Autoregressive orders:3 to 3
#> 
#> Maximum lags for TS  :3 to 3
# }

Bayesian Estimation of Multivariate TAR Models

Usage

Arguments

Value

See also

Examples