Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (1): 195-205.doi: 10.16088/j.issn.1001-6600.2021083003

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A Class of Autoregressive Moving Average Model with GARCH Type Errors

LIANG Xin1*, CHEN Xiaoling1, ZHANG Xingfa1,2, LI Yuan1,2   

  1. 1. School of Economics and Statistics, Guangzhou University, Guangzhou Guangdong 510006, China;
    2. Lingnan Research Institute of Statistical Science, Guangzhou University, Guangzhou Guangdong 510006, China
  • Received:2021-08-30 Revised:2021-09-15 Online:2022-01-25 Published:2022-01-24

Abstract: In this paper, an autoregressive moving average model with a new GARCH error term is proposed by combining DAR model and traditional ARMA-GARCH model. This model introduces more data information than the DAR model, and defines a new conditional heteroscedasticity structure driven by observable sequence, which is easier to estimate than the traditional ARMA-GARCH model. The article studies the quasi-maximum likelihood estimation of the model parameters, and proves the asymptotic normality of the estimator under weaker moment conditions. Numerical simulation results confirm the effective performance of the model under finite samples. Empirical research shows that this model can improve the data fitting effect, and has certain value of applications.

Key words: autoregressive moving average model, DAR model, quasi-maximum likelihood estimation, moment condition, asymptotic normality

CLC Number: 

  • O212.1
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