This book brings together a variety of non-Gaussian autoregressive-type models to analyze time-series data. This book collects and collates most of the available models in the field and provide their probabilistic and inferential properties. This book classifies the stationary time-series models into different groups such as linear stationary models with non-Gaussian innovations, linear stationary models with non-Gaussian marginal distributions, product autoregressive models and minification models. Even though several non-Gaussian time-series models are available in the literature, most of them are focusing on the model structure and the probabilistic properties.

The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.

Statistical image processing; application of the gibbs distribution to image segmentation; A model for orginal filtering of digital images; Spatial domain filtering of digital images; Spatial domain filters forimage processing; Edge detection by partitioning; A syntactic approach for SAR image nalysis; Parametric techniques for SAR image compression; Data compression of a first order intermittently excited AR process; A modular software for image information systems; A space-efficient hough transform implementation for object detection; New computing methods in image processing displays; Statistical graphics; Visualizing two-dimensional phenomena in four-dimensional space: A computer grahphics approach; The man-machine-graphics interface for statistical data analysis; Interactive color display methods for multivariate data; Interactive computer graphics in statistics; Illustrations of model diagnosis by means of three-dimensional biplots; Multivariate thin plate spline smoothing with positivity and other linear; Data analysis in three and four dimensions with nonparametric; Dimensionality reduction in density estimation; Volumetric 3-D displays and spatial perception; Index.

We study least absolute deviation (LAD) estimation for general autoregressive moving average time-series models that may be noncausal, noninvertible or both. For ARMA models with Gaussian noise, causality and invertibility are assumed for the parameterization to be identifiable. The assumptions, however, are not required for models with non-Gaussian noise, and hence are removed in our study. We derive a functional limit theorem for random processes based on an LAD objective function, and establish the consistency and asymptotic normality of the LAD estimator. The performance of the estimator is evaluated via simulation and compared with the asymptotic theory. Application to real data is also provided.