Predictive recursion maximum likelihood of threshold autoregressive model

Abstract

© Springer International Publishing AG 2017. In the threshold model, it is often the case that an error distribution is not easy to specify, especially when the error has a mixture distribution. In such a situation, standard estimation yields biased results. Thus, this paper proposes a flexible semiparametric estimation for Threshold autoregressive model (TAR) to avoid the specification of error distribution in TAR model. We apply a predictive recursion-based marginal likelihood function in TAR model and maximize this function using hybrid PREM algorithm. We conducted a simulation data and apply the model in the real data application to evaluate the performance of the TAR model. In the simulation data, we found that hybrid PREM algorithm is not outperform Conditional Least Square (CLS) and Bayesian when the error has a normal distribution. However, when Normal-Uniform mixture error is assumed, we found that the PR-EM algorithm produce the best estimation for TAR model.