This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.
In this paper, we are interested in exploring the dynamic causal relationships among two sets of three variables in different quarters. One set is futures sugar closing price in Zhengzhou futures exchange market （ZC）, spot sugar price in Zhengzhou （ZS） and futures sugar closing price in New York futures exchange market（NC） and the other includes futures sugar opening price in Zhengzhou （ZO）, ZS and NC. For each quarter, we first use Bayesian model selection to obtain the optimal causal graph with the highest BD scores and then use Bayesian model averaging approach to explore the causal relationship between every two variables. From the real data analysis, the two conclusions almost coincide, which shows that the two methods are practical.
We consider an Error-in-Variable partially linear model where the covariates of linear part are measured with error which follows a normal distribution with a known covariance matrix. We propose a corrected-loss estimation of the covariate effect. The proposed estimator is asymptotically normal. Simulation studies are presented to show that the proposed method performs well with finite samples, and the proposed method is applied to a real data set.
