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The absolute deterministic version of purchasing power parity (PPP), in which nominal exchange rates move precisely to offset changes in aggregate price levels between national economies, is not generally supported by empirical evidence. Testing PPP with standard regression models permits some stochastic "slippage" in the relation, but still yields little support for PPP. We argue in this paper that such tests do not correctly appraise in a statistical fashion the strength of the relations among prices and exchange rates. Using a development of Box and Tiao's canonical, correlation approach to cointegration, we find 11 significant stable relation among certain aggregate national price indices and the exchange rate between the US and Australia in a period of floating exchange rates. The sign of the relation is as advocated by PPP, although the size of the adjustment effect is lower. Furthermore, the relation breaks down at the time of known foreign exchange market intervention. The search procedure thus can be used to identify ex post the timing of switches in policy regimes.