Forecasting with univariate TAR models

Bayesian analysis of multivariate threshold autoregressive models with missing data

“…, it is possible to calculate: mean of the predictive distribution (point forecast), covariance matrix of the predictive distribution (measure of uncertainty of the forecast) and credible intervals for the point forecast. This procedure allows us to include the uncertainty of the parameters of the MTAR model in the forecast, which generalizes the forecasting procedure proposed by Nieto (2008) and Vargas (2012). In the following section we give ex post simulation examples for checking the performance of the forecasting procedure.…”

“…For this end, we need to find E[Y T +h |y 1:T , u 1:T , m], which is the best prediction in the sense of MMSE(minimum mean square error) for a model with m regimes and h ≥ 1. Nevertheless, an exact analytical expression of that conditional expectation is not easy to obtain in this context of non-linear models; this fact was pointed out in the Nieto's (2008) article for univariate TAR models. Therefore using Bayesian analysis and the quadratic loss function as the optimality criterion, we proceed to find the predictive distributions p(y T +h |y 1:T , u 1:T , m) for h ≥ 1 with which we can obtain the target conditional expectations.…”

“…The forecasts, credible intervals and the RVPD are shown on Table 6.10 based on a run of 15000 iterations with a burning period of 5000. All credible intervals take zeroes or positive values only, this is an important fact because the forecasting of the univariate TAR model in (Nieto, 2008) exhibited negative values in the credible intervals for the output vector in the hydrological application.…”

“…The convergence of the generated Markov chains is rapid. The forecasting was tackled by Nieto (2008), in both output and threshold variables finding the predictive distributions. Now, a new problem arises when we consider fitting vector time series with possible exogenous inputs to a Multivariate Threshold Autoregressive Model (MTAR) in the context of missing data.…”

Estimación de los modelos TAR cuando el proceso del ruido sigue una distribución t

“…Nieto (2005) diseñó una metodología bayesiana para la identificación y la estimación de los modelos TAR. Por otro lado, Nieto (2008) caracterizó los modelos TAR univariados en términos de la media, varianza, media condicional y varianza condicional, y concluyó que la varianza condicional en estos modelos no es constante, de donde se puede pensar a los modelos TAR como una alternativa a los modelos GARCH para describir la heterocedasticidad en los datos. Moreno (2010) comparó el ajuste de los modelos TAR con ruidos gaussianos siguiendo la metodología de Nieto (2005) con los modelos GARCH con ruidos t en series financieras de indicadores de bolsas de valores, y encontró que los modelos TAR con ruidos gaussianos pueden tener dificultades para capturar la heterocedasticidad marginal de la serie y no se ajustan tan bien como los modelos GARCH.…”