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Zhang, T., Wang, D. and Yang, K. (2021), Quasi-maximum exponential likelihood estimation for double-threshold GARCH models. Can J Statistics, 49: 1152-1178. https://doi.org/10.1002/cjs.11614
The generalized autoregressive conditional heteroscedastic (GARCH) models with thresholds have been widely used in lots of aspects within the past 20 years. Traditional model parameters estimation method, for example, the quasi-maximum likelihood estimation(QMLE), requires a strong moment condition of data. On the other hand, the time series data in economy or finance literature is not always match this strong condition, and which bring difficulty to practitioners research when they modelling and analysing real data. In this article, the nonparametric inference for the double-threshold GARCH (DTGARCH) models is considered. A better approach to estimating model parameters is applied by using quasi-maximum exponential likelihood estimation (QMELE). This estimation method relaxes the requirements of traditional method and does not make distributional assumptions about the error term in model. These advantages make this approach can be applied in extensive aspects of real data analysis. The article presents the results of simulation to assess the properties of the proposed approach compared to those of the traditional estimation method. The simulations show that the proposed method provides considerable and better performances. These performances are also illustrated in practical application on a financial time series data of stock returns.