mtarNAIC: Compute NAIC of a MTAR model

In adrincont/BMTAR: Bayesian Approach for MTAR Models with Missing Data

Description

Compute the Normalized Akaike information criteria (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 Normalized Akaike information criteria (NAIC) (Tong, 1990), in MTAR model. The NAIC for a MTAR model with l regimes is:

NAIC = {∑_{j = 1}^l AICj(r)}/{∑_{j = 1}^l N_j}

AICj(r) = Nj ln(|Sj/Nj|) + 2k η_j

Nj: number of observations in each regime.

S_{j}=∑_{t:j_t = j}(y_t-YP)'(y_t-YP)

YP = Φ_{0}^(j)+∑_{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}

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)

adrincont/BMTAR documentation built on Jan. 22, 2022, 2:09 p.m.