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Testing for co-nonlinearity

Abstract This article introduces the concept of co-nonlinearity. Co-nonlinearity is an example of a common feature in time series [Engle, Robert F., and Sharon Kozicki. 1993. “Testing for Common Features.” Journal of Business & Economic Statistics 11 (4): 369–380] and an extension of the concept of common nonlinear components [Anderson, Heather M., and Farshid Vahid. 1998. “Testing Multiple Equation Systems for Common Nonlinear Components.” Journal of Econometrics 84 (1): 1–36]. If some time series follow a nonlinear process but where a linear relationship between the levels of these series removes the nonlinearity, such a relationship is defined as co-nonlinear. In this article I show how to determine the number of such co-nonlinear relationships. Furthermore, I show how to formulate hypothesis tests on the co-nonlinear relationships in a full maximum likelihood framework. The framework for identifying co-nonlinear relationships is illustrated in a system of Norwegian interest rates.