A possible relationship between the Consumer Price Index and the Wholesale Price Index has been analyzed for long and short-run relationships. Conventional Engle and Granger [Estimation Test Econ. 55(1987) 2251-276] and Johansen's [J. Econ. Dyn. Control 12 (1988) 231-254] cointegration tests give mixed evidence for a possible long-run relationship between those two series. The model-free and seasonally robust periodogram-based test fails to reject the null of no-cointegration relationship. However, these two series move together in the short run. © 2005 Elsevier B.V. All rights reserved.