Non-Gaussian Markov time series
Srinivasa Patibandla Rao · Rice Research Repository (Rice University) · 1988
Time series are often modeled as filtered versions of white noise, the filter being linear. We study non-Gaussian processes by modeling them similarly, but allowing the possibility of the filter being non-linear. These processes are assumed to be first-order Markovian, and thus are completely described by their bivariate distributions. Series expansions of bivariate densities are shown to be a useful analytical tool to study these processes. We discuss the class of non-Gaussian processes that can be produced by linear filters, concentrating on a time series having hyperbolic secant amplitude distribution. Non-Gaussian time series are sensitive to the direction of the time axis and may have different statistical properties in the forward and backward directions. Measures sensitive to the direction of the time axis, such as the conditional mean, are demonstrated. We show that as a consequence of the temporal asymmetry of non-Gaussian linear models, prediction in the backward direction is always more accurate than prediction in the forward direction.