Testing Linearity for Network Autoregressive Models
Abstract
A quasiscore 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 chisquare and noncentral chisquare asymptotic distribution, respectively. These results still hold true when the parameters tested belong to the boundary of their space. When we deal with nonidentifiable parameters, a suitable test is proposed and its asymptotic distribution is established when the network dimension is fixed. Since, in general, critical values of such test cannot be tabulated, the empirical computation of the pvalues is implemented using a feasible bound. Bootstrap approximations are also provided. Moreover, consistency and asymptotic normality of the quasi maximum likelihood estimator is established for continuous and count nonlinear network autoregressions, under standard smoothness conditions. A simulation study and two data examples complement this work.
 Publication:

arXiv eprints
 Pub Date:
 February 2022
 arXiv:
 arXiv:2202.03852
 Bibcode:
 2022arXiv220203852A
 Keywords:

 Statistics  Methodology;
 Mathematics  Statistics Theory