梁湘三 (X. San Liang)博士
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 X1 and X2. The resulting formula for the information flow from X2 to X1, T2→1, turns out to be concise in form:
where Cij (i,j=1,2) is the sample covariance between Xi and Xj, and Ci,dj the covariance between Xi and , the difference approximation of dXj/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 CO2 and the global mean temperature anomaly. While it is confirmed that CO2 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.