基于分位数因子模型的高维时间序列因果关系分析

Causal relationship analysis of high⁃dimensional time series based on quantile factor model

从观察数据中发现变量之间的因果关系是许多科学研究领域的关键问题,传统Granger因果模型受到维度灾难的影响,难以准确地在高维时间序列中发现因果关系.提出一种基于分位数因子模型的Granger因果分析新方法QFMCGC用于高维时间序列因果关系的判定.首先,QFM-CGC采用赤池信息量准则进行模型选择,避免人为干预设置滞后阶数的操作;然后,对向量自回归(Vector Autoregressive,VAR)模型中的条件变量建立分位数因子模型进行降维,减少VAR模型中的待估计系数,对降维后的VAR模型重新进行条件Granger因果分析;最后,使用蒙特卡洛模拟评估不同方法识别底层系统与观测时间序列的连通性结构的能力.在不同维度变量的线性仿真系统和两组现实数据集上与基准方法和经典方法进行了比较,实验结果验证了该方法的有效性.

Finding the causal relationship between variables from observed data is a key issue in many scientific research fields.Because the traditional Granger causality model is affected by the curse of dimension,it is difficult to accurately find causality in high⁃dimensional time series.In this paper,we propose a new Granger causality analysis method based on quantile factor model,QFM⁃CGC algorithm,which is used to find causality relationship in high⁃dimensional time series.Firstly,QFM⁃CGC uses Akaike information criterion to select models,which avoids setting the lag order by human intervention.Then,the quantile factor model is established to reduce the dimensionality of the conditional variables in a vector autoregressive(VAR)model,thus reducing the number of coefficients that need to be estimated.The reduced⁃dimensional VAR model is used for a conditional Granger causality analysis.Finally,Monte Carlo simulation is applied to evaluate the performance of different methods to identify the connectivity structure between the underlying system and the observation time series.Experiments compare the proposed method with benchmark and classical methods on a linear simulation system with variables in different dimensions and two sets of real data,confirming its effectiveness.