The assumption of normality is commonly motivated in econometrics on the basis of the central limit theorem and the fact that much of the data is aggregated across time and across agents. However, most economic time series indicate non-normality in the form of either occasional big shocks or marked changes in the behavior of the series over different sub-periods (regime shifts). Gaussian processes have tails that are too thin to accommodate big shocks and they are too sluggish to learn about regime changes. The inability to effectively account for either of these features can be costly.
In this thesis infinite variance stable shocks which retain the central limit attributes as well as the advantages of continuity are used to model univariately the U.S. inflation rate, the value-weighted CRSP real stock returns, and the quarterly U.S. real GNP. We examine in detail the relationship between the level of inflation and its uncertainty, persistence in stock returns, and non-linearities and long memory in GNP.
Results indicate that the assumption of normality can be rejected for all three series. We find that inferences on the relationship between the level of inflation and its uncertainty are qualitatively and quantitatively sensitive to distributional assumptions. Stock returns fail to reveal a statistically significant mean-reverting component, after accounting for leptokurtosis, seasonality, and volatility persistence. Real GNP is characterized by a non-linear propagation mechanism, with little evidence of long memory. We also find that, in comparison to Gaussian models, stable models account for outliers and level shifts better, give more realistic assessment of uncertainty associated with such episodes, and provide tighter estimates of model parameters.