mtarns: Estimation of non-structural parameters for MTAR model

In BMTAR: Bayesian Approach for MTAR Models with Missing Data

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= φ^{(j)}_{0}+ ∑_{i=1}^{p_j} φ_{i}^{(j)}Y_{t-i}+ ∑_{i=1}^{q_j}β_{i}^{(j)}X_{t-i} + ∑{i=1}^{d_j}δ_{i}^{(j)}Z_{t-i} +Σ_{(j)}^{1/2} ε_{t} if r_{j-1}< Z_t ≤ r_{j},

where process \{ε_{t}\} is a k-variate independent Gaussian process, \{Y_t\} is k-variate process, \{X_t\} is a ν - variate process. The function implements Bayesian estimation of non-structural parameters of each regime j(φ^{(j)}_{0} φ_{i}^{(j)}, β_{i}^{(j)}, δ_{i}^{(j)} and Σ_{(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)

BMTAR documentation built on Jan. 19, 2021, 9:06 a.m.