Estimation of Regression Models with Multiple Structural Changes for Interval-valued Time Series Data

This paper studies the nonlinear features in interval-valued time series (ITS) data by considering a regression model with multiple structural changes. The number of structural changes is the critical parameter of the multiple change points analysis. By treating the determination of the number of structural changes as a model selection problem, a cross-validation (CV) method is proposed. The change points and regression coefficients are estimated by a minimum distance method based on DK distance. Both static and dynamic regression models for the ITS data are studied. Theoretical results for the proposed estimators are derived under some conditions. The finite-sample performance of the proposed estimators is assessed through Monte Carlo simulations. The empirical application studies the asymmetric impacts of the U.S. stock market on the U.K., Japan, and France stock markets.