December 2023 Nonlinear network autoregression
Mirko Armillotta, Konstantinos Fokianos
Author Affiliations +
Ann. Statist. 51(6): 2526-2552 (December 2023). DOI: 10.1214/23-AOS2345


We study general nonlinear models for time series networks of integer and continuous-valued data. The vector of high-dimensional responses, measured on the nodes of a known network, is regressed nonlinearly on its lagged value and on lagged values of the neighboring nodes by employing a smooth link function. We study stability conditions for such multivariate process and develop quasi-maximum likelihood inference when the network dimension is increasing. In addition, we study linearity score tests by treating separately the cases of identifiable and nonidentifiable parameters. In the case of identifiability, the test statistic converges to a chi-square distribution. When the parameters are not identifiable, we develop a supremum-type test whose p-values are approximated adequately by employing a feasible bound and bootstrap methodology. Simulations and data examples support further our findings.

Funding Statement

The research was supported by the European Regional Development Fund and the Republic of Cyprus through the Research and Innovation Foundation, under the project INFRASTRUCTURES/1216/0017 (IRIDA).


This work was completed when M. Armillotta was with the Department of Mathematics and Statistics at the University of Cyprus. We greatly appreciate comments made by the Editor, Assistant Editor and two reviewers on an earlier version of the manuscript.


Download Citation

Mirko Armillotta. Konstantinos Fokianos. "Nonlinear network autoregression." Ann. Statist. 51 (6) 2526 - 2552, December 2023.


Received: 1 November 2022; Revised: 1 July 2023; Published: December 2023
First available in Project Euclid: 20 December 2023

MathSciNet: MR4682707
zbMATH: 07783625
Digital Object Identifier: 10.1214/23-AOS2345

Primary: 62M10
Secondary: 62J02

Keywords: contraction , Hypothesis testing , increasing dimension , multivariate count time series

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.51 • No. 6 • December 2023
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