We investigate asymmetries in the conditional mean dynamics of U.S. GNP. Because the statistical evidence on nonlinearities in the conditional mean could be influenced by the presence of outliers or by a failure to model conditional heter oske dasticity, we explicitly account for outliers by assuming that the innovations are drawn from the stable family, and model time-varying volatility by a GARCH(1, 1) process. We also allow for the possibility of long memory in the series with fractional differencing. Our results indicate statistically significant nonlinearities in the conditional mean that persist even after accounting for these features in the data.

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