The Hypergeometric Process : A Flexible Parameterization of the Moving Average Process Time Series

We introduce an apparently new parameterisation of the Wold decomposition of a standard Box-Jenkins time series model in terms of the Hypergeometric Function pFq(.). This parameterization is sufficiently flexible to treat both finite standard ARMA(p, q) models and also fractionally integrated models such as FI(d). We demonstrate the parametric domain over which the process is variance stationary and also over which it is ergodic. We compute the autocovariance function for the general process and illustrate how the parameterization proposed here may be used to model other well known parameterizations of the MA(q) process