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This paper formulates a novel integrated measure for energy market efficiency, by investigating different perspectives of the market performance. Different from most existing models focusing on certain one perspective, the integrated measure especially takes all aspects into consideration, including self-similarity (or system memorability or long-term persistence) in terms of fractality, attractor properties in phase-space in terms of chaos, and disorder state of data dynamics in terms of entropy. In the proposed method, the most popular data analysis techniques of multi-fractal detrended fluctuation analysis, correlation dimension and sample entropy are respectively conducted on the market return data to capture the corresponding features; and then, the entropy weight method is used to generate the final integrated index. For illustration and verification, the proposed measure is applied to two typical energy markets, i.e., crude oil and carbon markets. Some interesting results can be found that the crude oil market (a comparatively mature and competitive market) can be shown more efficient than carbon market (an emerging market). Furthermore, the novel method can also offer much more information about the corresponding contribution of each aspect to the total efficiency

A Novel Integrated Measure for Energy Market Efficiency