A Generalized Information Theoretical Approach to Non-linear Time Series Model

Abstract

The limited data will bring about an underdetermined, or ill-posed problem for the observed data, or for regressions using small data set with limited data and the traditional estimation techniques are difficult to obtain the optimal solution. Thus the approach of Generalized Maximum Entropy (GME) is proposed in this study and applied it to estimate the kink regression model under the limited information situation. To the best of our knowledge, the estimation of kink regression model using GME has been not done yet. Hence, we extend the entropy linear regression to non-linear kink regression by modifying the objective and constraint functions under the context of GME. We use both Monte Carlo simulation and real data study to evaluate the performance of our estimation from Kink regression and found that GME estimator performs slightly better compared to the traditional Least squares and Maximum likelihood estimators.