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Limit Theorems for Weakly Dependent Non-stationary Random Field Arrays and Asymptotic Inference of Dynamic Spatio-temporal Models
- Publication Year :
- 2024
-
Abstract
- We obtain the law of large numbers (LLN) and the central limit theorem (CLT) for weakly dependent non-stationary arrays of random fields with asymptotically unbounded moments. The weak dependence condition for arrays of random fields is proved to be inherited through transformation and infinite shift. This paves a way to prove the consistency and asymptotic normality of maximum likelihood estimation for dynamic spatio-temporal models (i.e. so-called ultra high-dimensional time series models) when the sample size and/or dimension go to infinity. Especially the asymptotic properties of estimation for network autoregression are obtained under reasonable regularity conditions.
- Subjects :
- Mathematics - Statistics Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.07429
- Document Type :
- Working Paper