On the three‐step non‐Gaussian quasi‐maximum likelihood estimation of heavy‐tailed double autoregressive models

Abstract

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.

Pemodelan Jumlah Wisatawan Dengan Autoregressive Integrated Moving Average Dan Recurrent Artificial Neural Network

“…The results of the analysis show that RNN gives the best results in predicting the number of tourist arrivals. Gong and Li (2020) in their research results show that the ANN method gives the best results.…”

Bayesian inference for a mixture double autoregressive model

“…Financial time series data, such as stock returns, widely exists in our lives. Such data usually presents characteristics such as heteroscedasticity (Bollerslev, 1986; Engle, 1982), volatility clustering (Niu & Wang, 2013), large kurtosis (Alexander & Lazar, 2006), heavy‐tailed (Gong & Li, 2020), and asymmetry (Lisi, 2007; Zhang, Wang, & Yang, 2021). Among these characteristics the heteroscedasticity is the most typical one.…”

“…Liu, Li, and Kang (2018) investigated the sample path properties of an explosive DAR model. For some recent achievements on the DAR models, we refer to Zhu, Zhang, and Liang (2017), Zhu, Zheng, and Li (2018), Gong and Li (2020), Zhu and Li (2022), among others.…”

“…Liu, Li, and Kang (2018) investigated the sample path properties of an explosive DAR model. For some recent achievements on the DAR models, we refer to Zhu, Zhang, and Liang (2017), Zhu, Zheng, and Li (2018), Gong and Li (2020), Zhu and Li (2022), among others. Scholars have found that many financial time series exhibit features such as heavy-tailed, large kurtosis, extreme events and multimodal marginals.…”