Abstract
In the paper I continue investigations on the self-normalization of simple autoregressive field Xt,s = aXt−1,s + bXt,s−1 + εt,s started in [5]. And extend previous results when the variance of the innovations of the process above are not finite.
Highlights
Introduction and formulation of resultsThis paper continues the investigations of the self-normalization for the autoregressive fields on the plane which were started in [5]
In this paper the results for selfnormalization for AR(1) process obtained by Juodis and Rackauskas [4] were generalized for the autoregressive field on the plane
The results presented in [5] were proved under assumption of the the existence of the second moment for the innovations of the autoregressive field we are working with
Summary
This paper continues the investigations of the self-normalization for the autoregressive fields on the plane which were started in [5]. In this paper the results for selfnormalization for AR(1) process obtained by Juodis and Rackauskas [4] were generalized for the autoregressive field on the plane. The results presented in [5] were proved under assumption of the the existence of the second moment for the innovations of the autoregressive field we are working with. We give a slight extention of this result and prove that sufficient condition for our results to hold is that innovations belong to the domain of attraction of the normal law
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