Dynamic Conditional Correlation Models With Exogenous Variables

Time series exists in various areas,such as economics,financial engineering,environmental science,signal processing and pattern recognition,and the method to analyze the characteristics of data to extract meaningful and useful information has been widely studied.In the research of time series,the correlation of multivariate series is a factor of great importance,where dynamic conditional correlation(DCC)models can effectively describe the conditional correlation of series.In this paper,from the point of actual problems,we take into account the effect of exogenous variables on the correlation of series under study.We incorporate exogenous variables into the correlation equation of dynamic conditional correlation models,where the parameters in the equation change when the exogenous variables change,and this change can reflect the influence of exogenous variables on the conditional correlation of the series.The parameters added in the proposed model need no constraint to make sure of the positively of conditional correlation matrices.Further,an effective two-step maximum likelihood method is presented to estimate the parameters.Finally,simulation studies are conducted to illustrate the effectiveness of the proposed model and the model is applied to study the Asian stock market.The contents of the paper are as follows.In section 1,we review the propose of conditional heteroscedasticity and univariate and multivariate conditional heteroscedasticity models.In section 2,the constant conditional correlation model and dynamic conditional correlation model are described in detail.In section 3,the proposed model and corresponding parameter estimation approach are described in detail.In section 4,simulation studies are conducted to test the performance of the proposed method.In section 5,we use the proposed model to study the Asian stock market by treating American stock market as an exogenous variable,and analyze the experimental results.Some conclusions are covered in section 6.