On representation for nonGaussian ARMA processes

A generalised predictor space representation (of nonlinearity order two and memory M) for nonGaussian and nonminimum phase ARMA processes is proposed here, by expanding the underlying Hilbert space of finite L₂ norm random variables, which is now composed of linear combinations of linear as well as second order nonlinear terms of the process samples. Here the higher order statistical information enters into the picture in a natural way through the nonlinear terms. It is expected that the geometrical structure provided by the proposed predictor space would simplify the modeling of these processes. A set of new innovation vectors is defined on this space. Some of the properties of the new space are presented. The finite dimensionality of the proposed predictor space, when the underlying process admits a nonGaussian and nonminimum phase ARMA representation is proved. The application of the proposed theory to estimate nonGaussian and nonminimum phase ARMA process parameters is also discussed