BMTAR (version 0.1.1)

mtarmissing: Estimation of missing values of observed, covariate and threshold processes

Description

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

Usage

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

Arguments

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

Value

Return list type object of class “regime_missing”

tsregime

ini_obj$tsregime_obj with estimated observations

estimates

confident interval and mean of estimated missing values

Chain

if chain TRUE, chains of the estimated missing values

Details

The MTAR model

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

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 \(\alpha_t\), 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.

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<U+2013>318. doi:10.1080/03610926.2014.990758.

Examples

# NOT RUN {
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)))))
# }
# NOT RUN {
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]),]
# }