We investigate whether fluctuations in U.S. inflation rates are better described by infrequently occurring large shocks or by frequently occurring small shocks. We estimate a model that encompasses the two hypotheses within the framework of non-Gaussian state-space models. Our results indicate support for infrequently occurring large shocks, but this weakens somewhat once we allow for outliers and conditional heteroskedasticity. It appears that, for the purpose of forecasting monthly U.S. inflation rates, recognizing the distinction between frequent small shocks and infrequent large shocks does not matter much once outliers and conditional heteroskedasticity are allowed for.

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.