Autoregressive Modeling And Spectral Analysis of Array Data in the Plane

While a number of efficient statistical techniques exist for analysis of data recorded in time, this is to a lesser degree the case for spatial data such as seismological array data, magnetic data, or gravity data. In this paper we will be concerned with a new type of analysis for spatial variables. We will study autoregressive series F(x1, x2) in the plane defined by a unilateral expansion in the lower left-hand quadrant determined by the point (x1, x2). Using artificial data, we consider the problems of identification, fitting, and estimation for such series. Furthermore, we will indicate how one-quadrant autoregressive models may be used for approximating more general types of spatial data. In this connection we discuss the problem of stability and two criteria for determining the order (p1, p2) of the approximating model. Special consideration is given to the use of autoregressive approximations in spatial spectral density estimation and illustrations are given both for autoregressive series in the plane and for harmonic series. Based on our results we tentatively conclude that, as in the time series case, there are situations for data in the plane where autoregressive procedures are superior to the conventional spectral analysis methods.