Fourth-Moments Structures in Financial Time Series

Abstract: I consider a class of conditionally heteroskedastic models that comprises most linear "ARCH"-type models found in the literature. This class is especially motivated by the fact that two basic kinds of ARCH processes have been suggested in autocorrelated circumstances: Engle (1982) explains conditional variance by lagged errors, Weiss (1984) also by lagged observations. The general framework permits an evaluation of whether the restrictions evolving from the Engle or the Weiss models are valid in practice. My empirical example is a time series of 7000 observations of the Standard & Poor index including the "lunes negro" crash. Evidence is collected from parametric estimation of the outlined models and from an evaluation of descriptive fourth-moments estimates, for which significance bounds are established by means of algebra and simulation.;