mtarns {BMTAR}

Estimation of non-structural parameters for MTAR model

Description

Bayesian method for estimating non-structural parameters of a MTAR model with prior conjugate.

Usage

mtarns(ini_obj, level = 0.95, burn = NULL, niter = 1000,
chain = FALSE, r_init = NULL)

Arguments

ini_obj

class “regime_inipars” object, here specificate l and orders known, might know r or Sigma. Not NULL. Default l = 2, orders = list(pj = c(2,2))

level

numeric type, confident interval for estimations. Default 0.95

burn

numeric type, number of initial runs. Default NULL (30% of niter)

niter

numeric type, number of runs of MCMC. Default 1000

chain

logical type, if return chains of parameters. Default FALSE

r_init

numeric type of length l - 1. If r not known, starting value of the chain. Default NULL

Details

Based on the equation of the Multivariate Threshold Autoregressive(MTAR) Model

Y_t= \phi^{(j)}_{0}+ \sum_{i=1}^{p_j} \phi_{i}^{(j)}Y_{t-i}+ \sum_{i=1}^{q_j}\beta_{i}^{(j)}X_{t-i} + \sum{i=1}^{d_j}\delta_{i}^{(j)}Z_{t-i} +\Sigma_{(j)}^{1/2} \epsilon_{t} if r_{j-1}< Z_t \le r_{j},

where process \{\epsilon_{t}\} is a k-variate independent Gaussian process, \{Y_t\} is k-variate process, \{X_t\} is a \nu - variate process. The function implements Bayesian estimation of non-structural parameters of each regime j(\phi^{(j)}_{0} \phi_{i}^{(j)}, \beta_{i}^{(j)}, \delta_{i}^{(j)} and \Sigma_{(j)}^{1/2}) is carried out. The structural parameters: Number of Regimes(l), Thresholds(r_1,\cdots,r_{l-1}), and autoregressive orders(p_j,q_j,d_j) must be known. Prior distributions where selected in order to get conjugate distributions.

Value

Return a list type object of class “regime_model”

Nj

number of observations in each regime

estimates

list for each regime with confident interval and mean value of the parameters

regime

“regime” class objects with final estimations

Chain

if chain TRUE list type object with parameters chains

fitted.values

matrix type object with fitted.values of the estimated model

residuals

matrix type object with residuals of the estimated model

logLikj

log-likelihood of each regime with final estimations

data

list type object $Yt and $Ut = (Zt,Xt)

r

final threshold value with acceptance percentage or r if known

orders

list type object with names (pj,qj,dj) known

Author(s)

Valeria Bejarano [e-mail], Sergio Calderon [e-mail] & Andrey Rincon [e-mail]

References

Calderon, S. and Nieto, F. (2017) Bayesian analysis of multivariate threshold autoregress models with missing data. Communications in Statistics - Theory and Methods 46 (1):296–318. doi:10.1080/03610926.2014.990758.

Examples

data("datasim")
data = datasim
#r known
parameters = list(l = 2,
                  orders = list(pj = c(1,1)),
                  r = data$Sim$r)
initial = mtarinipars(tsregime_obj = data$Sim,
                      list_model = list(pars = parameters))

estim1 = mtarns(ini_obj = initial,niter = 1000,chain = TRUE)
print.regime_model(estim1)
autoplot.regime_model(estim1,2)
autoplot.regime_model(estim1,3)
autoplot.regime_model(estim1,5)
diagnostic_mtar(estim1)

#r unknown
parameters = list(l = 2,orders = list(pj = c(1,1)))
initial = mtarinipars(tsregime_obj = data$Sim,
list_model = list(pars = parameters))

estim2 = mtarns(ini_obj = initial,niter = 500,chain = TRUE)
print.regime_model(estim2)
autoplot.regime_model(estim2,1)
autoplot.regime_model(estim2,2)
autoplot.regime_model(estim2,3)
autoplot.regime_model(estim2,5)
diagnostic_mtar(estim2)