In this paper we propose a generalized version of the RESET test for linearity in regressions with
I(1) processes against various nonlinear alternatives and no cointegration. The proposed test statistic
for linearity is given by the Wald statistic and its limiting distribution under the null hypothesis of
linearity is shown to be a 2 distribution when a "leads and lags" estimation technique is employed
to construct the test statistic. We show that the test is consistent against a class of nonlinear alternatives
and no cointegration. This class includes polynomial functions of finite order, the logarithmic
function, and the distribution function of any random variable and its scalar multiple. Finite-sample
simulations show that the empirical size of the test is close to the nominal one and the test succeeds in
detecting both nonlinearity in the class and no cointegration. We apply the test to see if relationships
between exchange rates and fundamentals are linear and find significant evidence against linearity
for all countries considered.
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