This article introduces the concept of cononlinearity. Cononlinearity is an example of a common feature in time series (Engle and Koziciki, 1993, J. Bus. Econ. Statist.) and an extension of the concept of common nonlinear components (Anderson and Vahid, 1998, J. Econometrics). If some time series follow a nonlinear process but there exists a linear relationship between the levels of these series that removes the nonlinearity, then this relationship is said to be a cononlinear relationship. In this article I show how to determine the number of such cononlinear relationships. Furthermore, I show how to formulate hypothesis tests on the cononlinear relationships in a full maximum likelihood framework.

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