mtarNAIC {BMTAR}

Compute NAIC of a MTAR model

Description

Compute the Non-linear Akaike information criterion (NAIC) of a “regime_model” class object.

Usage

mtarNAIC(regimemodel)

Arguments

regimemodel

object of class “regime_model”

Details

Estimation of thresholds was made before starting the Bayesian procedure via the Non-linear Akaike information criterion (NAIC) (Tong, 1990), in MTAR model. The NAIC for a MTAR model with l regimes is:

NAIC = {\sum_{j = 1}^l AICj(r)}/{\sum_{j = 1}^l N_j}

AICj(r) = Nj ln(|Sj/Nj|) + 2k \eta_j

Nj: number of observations in each regime.

S_{j}=\sum_{t:j_t = j}(y_t-YP)'(y_t-YP)

YP = \Phi_{0}^(j)+\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}

Value

Return a list type object:

AICj

numeric type, AIC for each regime

NAIC

numeric type, NAIC value

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
# Estimate number of regimes with NAIC
initial1 = mtarinipars(tsregime_obj = data$Sim,
list_model = list(pars = list(l = 2,
orders = list(pj = c(1,1),dj = c(1,1)), r = 0.2)))
estruc1 = mtarns(ini_obj = initial1,niter = 100,chain = TRUE,burn = 100)

initial2 = mtarinipars(tsregime_obj = data$Sim,
list_model = list(pars = list(l = 2,
orders = list(pj = c(1,1),dj = c(1,1)), r = 0.3)))
estruc2 = mtarns(ini_obj = initial2,niter = 100,chain = TRUE,burn = 100)
#NAIC
mtarNAIC(estruc1)
mtarNAIC(estruc2)