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On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models
Author(s) -
Gong Huan,
Li Dong
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12525
Subject(s) - mathematics , autoregressive model , estimator , consistency (knowledge bases) , strong consistency , asymptotic distribution , gaussian , statistics , least absolute deviations , star model , econometrics , autoregressive integrated moving average , time series , physics , geometry , quantum mechanics
This note considers a three‐step non‐Gaussian quasi‐maximum likelihood estimation (TS‐NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy‐tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy‐tailed.