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 the

more »

... mean. Evidence on long memory is weak, and is sensitive to the specification of the short-run dynamics. Linear Gaussian models, and non-linear conditionally heteroskedastic models of the GARCH class, seem inadequate for understanding the dynamics of this time series.