Asymptotics for the conditional self-weighted M $$ M $$ estimator of GRCA( p $$ p $$ ) models and its statistical inference

Under the $p$-order generalised random coefficient autoregressive (GRCA($p$)) model with random coefficients ${\Phi }_t,$ we propose a conditional self-weighted $M$ estimator of $E{\Phi }_t$. We investigate the asymptotic normality of this estimator with possibly heavy-tailed random variables. Furthermore, a Wald test statistic is constructed for the linear restriction on the parameters. In addition, the simulation experiments are carried out to assess the finite sample performance of theoretical results. Finally, a real data analysis about the increase (%) in the number of construction projects this year over the same period of last year is provided.