Measuring U.S. Business Cycle Using Markov-Switching Model: A Comparison Between Empirical Likelihood Estimation and Parametric Estimations

Abstract

Markov-switching (MS) model is one of the most popular nonlinear time series models in the literature. However, as there are many methods for parameter estimation, the results including the plot are not similar and become more difficult for researchers to decide on the interpretation. Therefore, this study is conducted as we want to obtain a more sensitive estimation method for the MS model. This study attempts to improve the way we estimate the MS model by developing a more flexible estimator for it to be called a maximum empirical likelihood estimation (MELE). A key point of this method is that a conventional parametric likelihood is replaced by the empirical likelihood function with relatively minor modifications to existing recursive filters. To evaluate the new method’s performance, we apply the MS model to the U.S. business cycle. The estimated results from the MELE are discussed and compared to those from classical parametric estimations. It is found that the empirical likelihood could outperform the classical likelihood estimators.