mtarns {BMTAR} R Documentation

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 vbejaranos@unal.edu.co, Sergio Calderon sacalderonv@unal.edu.co & Andrey Rincon adrincont@unal.edu.co

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)



[Package BMTAR version 0.1.1 Index]