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Reconsidering ergodicity and fundamental uncertainty

机译:重新考虑遍历性和基本不确定性

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This paper studies the relationships between the concepts of ergodicity, stationarity, homogeneity, and Keynesian fundamental uncertainty in light of a recent debate between Rod O'Donnell (2014-15) and Paul Davidson (2015). The latter has long argued that Keynesian fundamental uncertainty is best viewed as an axiomatic ontological condition of nonergodicity of a system. This influential view is challenged by O'Donnell who favors an epistemological behavioral perspective based on people having imperfect knowledge. Whereas for Davidson it is Keynes overthrowing the axiom of ergodicity that is fundamental, for O'Donnell it is Keynes overthrowing the axiom of perfect knowledge. We shall find that both parties make valid points in this debate, but further clarification is needed. Both accept that while Keynes never used the term ergodicity in his writings, he did discuss problems of nonhomogeneity of data when critiquing the econometric methodology of Jan Tinbergen. While it is known that a stationary series may be nonergodic, such as a limit cycle, it is much less well known and not commented on by either of them that a nonstationary series may be ergodic. Furthermore, while a nonstationary series must be nonhomogeneous, a nonhomogeneous series may be stationary under proper transformations such as first differencing. Deeper connections of the development of ergodic theory and chaos theory and this link to the debate over fundamental uncertainty are also discussed.
机译:鉴于Rod O'Donnell(2014-15)和Paul Davidson(2015)之间最近的争论,本文研究了遍历性,平稳性,同质性和凯恩斯主义基本不确定性之间的关系。后者长期以来一直认为,凯恩斯主义的基本不确定性最好被视为系统非遍历性的公理本体论条件。这种有影响力的观点遭到了奥唐纳的挑战,奥唐纳主张基于知识不完善的人们的认识论行为观点。对于戴维森而言,凯恩斯推翻了基本的遍历公理,而对奥唐奈而言,凯恩斯推翻了完美知识的公理。我们将发现双方在这场辩论中都提出了正确的观点,但是有必要进一步澄清。双方都承认,尽管凯恩斯在其著作中从未使用过“遍历性”一词,但他在批评扬·廷伯根的计量经济学方法时确实讨论了数据的非均质性问题。虽然已知平稳序列可能是非遍历的,例如极限环,但众所周知的很少,并且没有一个人评论非平稳序列可能是遍历的。此外,虽然非平稳序列必须是非齐次的,但在适当的变换(例如一阶微分)下,非齐次系列可能是平稳的。还讨论了遍历理论和混沌理论发展的更深层次的联系,以及与基本不确定性辩论的联系。

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