梁湘三 (X. San Liang)博士

南京信息工程大学海洋科学学院教授 江苏特聘教授

__2002____年 美国哈佛大学应用数学及物理海洋学博士__

个人网页：http://web2.nuist.edu.cn/hyxy/2012-3/2012330133743.html

Given two time series, can one faithfully tell, in a __rigorous__ and __quantitative__ way, the cause and effect between them? With a recently rigorized notion namely information flow/transfer, we show that this important and challenging question, which is of interest in a wide variety of disciplines, has a positive answer. Here causality is measured by the time rate of information transferring from one series to the other. Let the series be *X*_{1} and *X*_{2}. The resulting formula for the information flow from *X*_{2} to *X*_{1}, *T*_{2→1}, turns out to be concise in form:

where *C*_{ij} (*i,j=1,*2) is the sample covariance between *X*_{i }and *X*_{j}, and *C*_{i,dj} the covariance between *X*_{i} and , the difference approximation of *d**X*_{j}*/dt* using the* Euler forward scheme*. An immediate corollary is that causation implies correlation, but not vice versa, resolving the long-standing debate over causation versus correlation.

The above formula has been validated with touchstone series purportedly generated with one-way causality that evades the classical approaches such as Granger causality test and transfer entropy analysis. It has also been applied successfully to the investigation of many real problems. Through a simple analysis with the stock series of IBM and GE, an unusually strong one-way causality is identified from the former to the latter in their early era, revealing to us an old story, which has almost faded into oblivion, about “Seven Dwarfs” competing with a “Giant” for the computer market.

Another example presented here regards the cause-effect relation between the two climate modes, El Niño and Indian Ocean Dipole (IOD). In general, these modes are mutually causal, but the causality is asymmetric. To El Niño, the information flowing from IOD manifests itself as a propagation of uncertainty from the Indian Ocean.

In the third example, an unambiguous one-way causality is found between CO_{2} and the global mean temperature anomaly. While it is confirmed that CO_{2} indeed drives the recent global warming, on paleoclimate scales the cause-effect relation may be completely reversed.

Also will be mentioned are a few other applications, e.g., a simple pattern underlying a chaotic attractor, and a study of the causal structure in the near-wall turbulence.