Estimation of non-structural parameters for MTAR model
Bayesian method for estimating non-structural parameters of a MTAR model with prior conjugate.
mtarns(ini_obj, level = 0.95, burn = NULL, niter = 1000, chain = FALSE, r_init = NULL)
ini_obj |
class “ |
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 |
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.
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 |
“ |
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 $Ut = (Zt,Xt) |
r |
final threshold value with acceptance percentage or r if known |
orders |
list type object with names (pj,qj,dj) known |
Valeria Bejarano vbejaranos@unal.edu.co, Sergio Calderon sacalderonv@unal.edu.co & Andrey Rincon adrincont@unal.edu.co
Calderon, S. and Nieto, F. (2017) Bayesian analysis of multivariate threshold autoregress models with missing data. Communications in Statistics - Theory and Methods 46 (1):296–318. doi:10.1080/03610926.2014.990758.
data("datasim")
data = datasim
#r known
parameters = list(l = 2,
orders = list(pj = c(1,1)),
r = data$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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.