Abstract
In, Tory and Pickard show that a simple subclass of unilateral AR processes identifies with Gaussian Pickard random fields on Z 2. First, we extend this result to the whole class of unilateral AR processes, by showing that they all satisfy a Pickard-type property, under which correlation matching and maximum entropy properties are assessed. Then, it is established that the Pickard property provides the ‘missing’ equations that complement the two-dimensional Yule-Walker equations, in the sense that the conjunction defines a one-to-one mapping between the set of AR parameters and a set of correlations. It also implies Markov chain conditions that allow exact evaluation of the likelihood and an exact sampling scheme on finite lattices.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.