# Testing Linearity for Network Autoregressive Models

@inproceedings{Armillotta2022TestingLF, title={Testing Linearity for Network Autoregressive Models}, author={Mirko Armillotta and Konstantinos Fokianos}, year={2022} }

A quasi-score linearity test for continuous and count network autoregressive models is developed. We establish the asymptotic distribution of the test when the network dimension is fixed or increasing, under the null hypothesis of linearity and Pitman’s local alternatives. When the parameters are identifiable, the test statistic approximates a chi-square and noncentral chi-square asymptotic distribution, respectively. These results still hold true when the parameters tested belong to the…

## 2 Citations

### The R-package PNAR for modelling count network time series

- Mathematics, Computer Science
- 2022

A new R package for analysis and inference of network count time series, providing users the ability to study and specify non-linear network counttime series models by providing them with a toolkit that copes with computational issues.

### Some recent trends in embeddings of time series and dynamic networks

- Computer Science
- 2022

This paper gives a review of some recent developments in embeddings of time series and dynamic networks and highlights diﬀerences between the static and dynamic case, and point to several open problems in the dynamic case.

## References

SHOWING 1-10 OF 78 REFERENCES

### Estimation and testing linearity for non-linear mixed poisson autoregressions

- Mathematics
- 2015

Non-linear mixed Poisson autoregressive models are studied for the analysis of count time series. Given a correct mean specification of the model, we discuss quasi maximum likelihood estimation based…

### Testing a linear time series model against its threshold extension

- Mathematics, Computer Science
- 2011

A novel bootstrap approximation based on stochastic permutation is proposed, which is robust to the assumptions on the error term, and enjoys more flexibility and needs less computation when compared with methods currently used in the literature.

### Multivariate count autoregression

- Mathematics, Computer ScienceBernoulli
- 2020

A novel conceptual framework based on copulas is developed for studying the properties of multivariate count time series data with Poisson marginals, which avoids conceptual difficulties resulting from the joint distribution of discrete random variables.

### Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis

- Mathematics, Economics
- 1996

Many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses. This paper studies the asymptotic distribution theory for such tests. The asymptotic…

### Testing linearity against smooth transition autoregressive models

- Mathematics
- 1988

SUMMARY We study a general univariate smooth transition autoregressive, STAR, model. It contains as a special case the self-exciting threshold autoregressive, SETAR, model. We present three tests for…

### Specification testing in nonlinear and nonstationary time series autoregression

- Mathematics
- 2009

This paper considers a class of nonparametric autoregressive models with nonstationarity. We propose a nonparametric kernel test for the conditional mean and then establish an asymptotic distribution…

### Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models

- Mathematics
- 2017

We study a general class of quasi-maximum likelihood estimators for observation-driven time series models. Our main focus is on models related to the exponential family of distributions like Poisson…

### Grouped Network Vector Autoregression

- Mathematics
- 2020

In the study of time series analysis, it is of great interest to model a continuous response for all the individuals at equally spaced time points. With the rapid advance of social network sites,…

### Network GARCH Model

- Computer Science
- 2020

A network GARCH model is proposed that uses information derived from an appropriately defined network structure that decreases the number of unknown parameters and reduces the computational complexity substantially.

### SUP-TESTS FOR LINEARITY IN A GENERAL NONLINEAR AR(1) MODEL

- MathematicsEconometric Theory
- 2009

We consider linearity testing in a general class of nonlinear time series models of order one, involving a nonnegative nuisance parameter that (a) is not identified under the null hypothesis and (b)…