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Recently, a new linearity test for time series was introduced based on concepts from the theory of neural networks. Lee et al. have already studied the power properties of this test and they are further investigated here. They are compared by simulation with those of a Lagrange multiplier (LM) type test that we derive from the same single-hidden-layer neural network model. The auxiliary regression of our LM type test is a simple cubic 'dual' of the Volterra expansion of the original series, and the power of the test appears superior overall to that of the other test.

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