Abstract
As the big data science develops, efficient methods are demanded for various data analysis. Granger causality provides the prime model for quantifying causal interactions. However, this theoretic model does not meet the requirement for real-world data analysis, because real-world time series are diverse whose models are usually unknown. Therefore, model-free measures such as information transfer measures are strongly desired. Here, we propose the multi-scale extension of conditional mutual information measures using MORLET wavelet, which are named the WM and WPM. The proposed measures are computational efficient and interpret information transfer by multi-scales. We use both synthetic data and real-world examples to demonstrate the efficiency of the new methods. The results of the new methods are robust and reliable. Via the simulation studies, we found the new methods outperform the wavelet extension of transfer entropy (WTE) in both computational efficiency and accuracy. The features and properties of the proposed measures are also discussed.
Highlights
As big data science developments, practical time series methods are demanded to study the complexity and dynamics of the data
Real-world data are time series usually obtained by experiments or observations whose models are diverse and the data are often nonlinear or non-stationary [1,2], e.g. the EEG time series measured from experiments [2,3,4,5] and financial data observed from real-world markets [6]
The conditional Granger causality is a multivariate method that can detect direct interactions between time series [10], the frequency domain GC is derived for frequency domain data analysis [10,11], and the nonlinear GC can be applied to nonlinear data analysis [12]
Summary
As big data science developments, practical time series methods are demanded to study the complexity and dynamics of the data. Various directed methods have been developed for studying the directed interaction between time series. The most classic causality measure is the Granger causality (GC) [7,8], it is a prime model for causality measures which uses significance tests to detect the directed dependency of one time series on another time series [7,8]. The conditional Granger causality is a multivariate method that can detect direct interactions between time series [10], the frequency domain GC is derived for frequency domain data analysis [10,11], and the nonlinear GC can be applied to nonlinear data analysis [12].
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