论文标题
与协方差或相关性的非平稳高斯或代数波动的确切多元振幅分布
Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations
论文作者
论文摘要
复杂的系统通常是非平稳的，典型的指标正在不断改变时间序列的统计特性。特别是，不同时间序列之间的相关性波动。描述此类系统的多元振幅分布的模型引起了极大的兴趣。扩展了先前的工作，我们将一组测得的非平稳相关矩阵视为一个集合，我们为其设置了随机矩阵模型。我们使用此合奏来平均在短时间尺度上测量的固定多元振幅分布，从而获得具有重型尾巴的大尺度的多元振幅分布。我们明确解决了四个案例，结合了高斯和代数分布。结果是封闭形式或单个积分。因此，我们首先为此类非平稳系统提供明确的多元分布，其次，该工具可定量捕获相关性中的非平稳性程度。
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate amplitude distributions of such systems are of considerable interest. Extending previous work, we view a set of measured, non-stationary correlation matrices as an ensemble for which we set up a random matrix model. We use this ensemble to average the stationary multivariate amplitude distributions measured on short time scales and thus obtain for large time scales multivariate amplitude distributions which feature heavy tails. We explicitly work out four cases, combining Gaussian and algebraic distributions. The results are either of closed forms or single integrals. We thus provide, first, explicit multivariate distributions for such non-stationary systems and, second, a tool that quantitatively captures the degree of non-stationarity in the correlations.
