Identification of Wiener Model with Internal Noise Using a Cubic Spline Approximation-Bayesian Composite Quantile Regression Algorithm

Abstract

A cubic spline approximation-Bayesian composite quantile regression algorithm is proposed to estimate parameters and structure of the Wiener model with internal noise. Firstly, an ARX model with a high order is taken to represent the linear block; meanwhile, the nonlinear block (reversibility) is approximated by a cubic spline function. Then, parameters are estimated by using the Bayesian composite quantile regression algorithm. In order to reduce the computational burden, the Markov Chain Monte Carlo algorithm is introduced to calculate the expectation of parameters’ posterior distribution. To determine the structure order, the Final Output Error and the Akaike Information Criterion are used in the nonlinear block and the linear block, respectively. Finally, a numerical simulation and an industrial case verify the effectiveness of the proposed algorithm.

Time‐ and Quantile‐Varying Causality between Investor Attention and Bitcoin Returns: A Rolling‐Window Causality‐in‐Quantiles Approach

“…In recent years, quantile-related methods have been widely used in economics and management [27,[48][49][50]. Among them, the quantile causality test is a new methodology used to test the nonlinear causality between variables.…”