Nonstationary Time Series, Cointegration, and the Principle of the Common Cause

Abstract

Elliot Sober ([2001]) forcefully restates his well-known counterexample to Reichenbach's principle of the common cause: bread prices in Britain and sea levels in Venice both rise over time and are, therefore, correlated; yet they are ex hypothesi not causally connected, which violates the principle of the common cause. The counterexample employs nonstationary data—i.e., data with time-dependent population moments. Common measures of statistical association do not generally reflect probabilistic dependence among nonstationary data. I demonstrate the inadequacy of the counterexample and of some previous responses to it, as well as illustrating more appropriate measures of probabilistic dependence in the nonstationary case. 1. A challenge to the principle of the common cause 2. Sober's argument and the attempts to rescue the principle 3. Probabilistic dependence 4. Nonstationary time series 5. Probabilistic dependence in nonstationary time series 6. Do Venetian sea levels and British bread prices violate the principle of the common cause?

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