mtarmissing: Estimation of missing values of observed, covariate and...
In adrincont/BMTAR: Bayesian Approach for MTAR Models with Missing Data

Description Usage Arguments Details Value Author(s) References Examples

Estimation using Bayesian methodology of missing values in observed(output), covariate and threshold processes.

1 2	mtarmissing(ini_obj,niter = 1000, chain = FALSE, level = 0.95, burn = NULL, cU = 0.5, b = NULL)

`ini_obj`	class “`regime_inipars`” object, here specificate in pars: l, orders and r known. Not NULL
`niter`	numeric type, number of runs of MCMC. Default 1000
`chain`	logical type, if return chains of parameters. Default FALSE
`level`	numeric type, confident interval for estimations. Default 0.95
`burn`	numeric type, number of initial runs. Default NULL (10% of niter)
`cU`	numeric type, coefficient of the diagonal covariance matrix of process Ut = (Zt,Xt). Default 0.5
`b`	numeric type greater or equal 1, autoregressive order of Ut = (Zt,Xt). Default NULL meaning 1

The 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},

is written into a state space model with regime-switching where the matrices depend on the threshold variable. In order to estimate the missing data in the observed vector Y_t, it is necessary to obtain samples of the full conditional distribution of the state vector α_t, for all times t=1,\cdots,T using Kalman Filter. It is assumed that the process U_t=(X_t,Z_t) is a Markov chain, and in order to get samples of the full conditional distribution of U_t, t=1,\cdots,T, it is supposed that kernel and initial distribution are Gaussian for simplicity. However, in the next updates, we are going to get flexibility at this point.

Return list type object of class “regime_missing”

`tsregime`	ini_obj$tsregime_obj with estimated observations
`estimates`	credibility interval and mean of estimated missing values
`Chain`	if chain TRUE, chains of the estimated missing values
`pos_na`	list for where are the missing values in each process (Yt and Ut)

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")
yt = datasim$Sim
# some missing data
data_yt = yt$Yt
data_zt = yt$Zt
posNA = sample(c(1:500),8)
data_yt[c(posNA),] = c(NA,NA)
posNA = sample(c(1:500),8)
data_zt[c(posNA)] = NA
data_final = tsregime(data_yt,data_zt,r = yt$r)
autoplot.tsregime(data_final,1)
autoplot.tsregime(data_final,2)

initial = mtarinipars(tsregime_obj = data_final,
list_model = list(pars = list(l = 2,r = datasim$Sim$r,
orders = list(pj = c(1,1), qj = c(0,0),dj = c(0,0)))))

missingest = mtarmissing(ini_obj = initial,chain = TRUE,
niter = 500,burn = 500)
print(missingest)
autoplot.regime_missing(missingest,1)
datasim$Sim$Yt[is.na(data_yt[,1]),]
missingest$tsregime$Yt[is.na(data_yt[,1]),]