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We examine quarterly U.S. real GNP data for evidence of non-linearity and long memory. Since the statistical evidence on non-linearities in the conditional mean could be influenced by the presence of outliers, or by a failure to model changing volatilities, 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. Our results indicate statistically significant non-linearities in thedoi:10.2139/ssrn.2076 fatcat:cpquv42iavcsharunoeirgs6eq