| The autoregressive conditional heteroskedastic (ARCH) model [Engle, 1982] and its generalized version (LARCH) (Bollerslev, 1986 are now not only widely used in modeling financial data but also provide a benchmark to evaluate other available models in empirical studies. The classical feature of this class of models is that the conditional variance (second moment) is considered to be time varying. ARCH models are generally estimated assuming conditional error distribution as normal. Therefore, under this set up, the standardized residuals are supposed to behave like IID N(0,1). Several studies, including Hansen (1994), Lye, Martin and Teo (1996), and Harvey and Siddique (1999), argue that there is no reason to believe standardized residuals to be independent of the conditioning information. They argue that it is reasonable to expect that skewness and kurtosis also depend upon the conditioning information. This dissertation addresses the non-normal behavior of standardized residuals by suggesting a model which incorporates skewness and kurtosis using the venerable, but previously little used, Pearson type IV distribution. The Pearson type IV distribution has not been used in any major applied work, including econometrics and finance literature because it was perceived to be complicated [Stuart and Ord, 1994, page 222]. Given the recent advances in computation, I find that the use of type IV distribution is no more difficult than the use of Student's t-distribution, and the flexibility of type IV density enables me to capture many of the stylized facts of financial data that have been difficult to account for with earlier parametric specifications. In this dissertation, I also provide details on the properties of Pearson type IV distribution, and indicate its versatility and usefulness in analyzing economic and financial data. As a by-product of my investigation I suggest a new test for symmetry, and adjustments for the standard tests for skewness and kurtosis. |
