  We propose a simple stochastic process for modeling improper or noncircular
complex-valued signals. The process is a natural extension of a complex-valued
autoregressive process, extended to include a widely linear autoregressive
term. This process can then capture elliptical, as opposed to circular,
stochastic oscillations in a bivariate signal. The process is order one and is
more parsimonious than alternative stochastic modeling approaches in the
literature. We provide conditions for stationarity, and derive the form of the
covariance and relation sequence of this model. We describe how parameter
estimation can be efficiently performed both in the time and frequency domain.
We demonstrate the practical utility of the process in capturing elliptical
oscillations that are naturally present in seismic signals.
