Asymptotics for the conditional self-weighted M-estimator of GRCA(1) models with possibly heavy-tailed errors

Geometric ergodicity and conditional self‐weighted M‐estimator of a GRCAR(p) model with heavy‐tailed errors

“…Secondly, the 𝜔 t allow us to approximate L n ( φn ) by a quadratic form. In addition, Theorem 2.4 generalizes the results of Ling (2005), Wang and Hu (2017) and Fu et al (2021).…”

“…In addition, Theorem 2.4 generalizes the results of Ling (2005), Wang and Hu (2017) and Fu et al . (2021).…”

“…Yang and Ling (2017) investigated the self-weighted least absolute deviation estimation for heavy-tailed threshold autoregressive models. Fu et al (2021) studied the asymptotic properties for the conditional self-weighted M-estimator of GRCAR(1) model with possibly heavy-tailed errors. However, general easy-to-check conditions for stationarity and limiting distributions of robust parameter estimators for statistical inference of GRCAR(p) with heavy-tailed errors are still open problems.…”

“…Moreover, the stationarity conditions for GRCAR(p) are implied as a corollary of our general result. Second, motivated by Yang and Ling (2017), Ling (2005), Wang and Hu (2017) and Fu et al (2021), we prove the asymptotic property of a self-weighted M-estimator (SM-estimator) for GRCAR(p) with possible infinite variance, and show that the limiting distribution of SM-estimator is asymptotically normal. Simulation results and a real data example are given to support our methodology.…”

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

“…The variable selection problem of the GRCA model was researched by Zhao, Liu & Peng (2018). Based on GRCA(1) model, Fu et al (2021) gave the asymptotically normality of conditional self-weighted M estimator.…”