Abstract: There are serious structural changes in the macroeconomic field. The performance of the model estimators is sensitive to the choice of estimation sample size, while methods to select the window size in rolling time-varying parameter model have received little attention.In this paper, a new approach is developed to select the rolling bandwidth for capturing the time-varying parameter in models with potential breaks. More specifically, the function forms are unknown, which can be set as a single-index semi-parametric model that can capture the linear or nonlinear relationship between variables, also can be extended to the linear or generalized linear regression model where only need to use the corresponding model estimation method.
Our new approach, to balance the accuracy and the time-varying objectives of the model estimators, solves the multi-objective optimization problem that minimizing bootstrap approximation quadratic loss function of model estimators and maximizing the Manhattan distance between the sub-sample estimators. Monte Carlo simulations show that using the window size selected by our procedure can significantly improve upon the performance of the model estimators. And also our method is applicable to all kinds of structural changes and time-varying parameter models of linear and nonlinear relations, not sensitive to the parameters choice in the same data generation process.When applied to capture the structural changes of China's financial network, 30 financial institutions, from 16 October, 2010 to 26 September, 2015, are included. Our results suggest that our procedure can capture the structural changes of the financial system, also significantly improve upon the performance of the financial network model estimators compared to traditional methods which just according to the subjective intention and forecasting performance. Our research and conclusions are helpful for the optimization and application of time-varying parameter model, and have important theoretical value and practical significance.

Key words: rolling bandwidth selection, time-varying parameter model, bootstrap estimation, financial network