Quasi‐maximum exponential likelihood estimation for double‐threshold GARCH models

Abstract

We consider the nonparametric inference for the double‐threshold generalized autoregressive conditional heteroscedastic models. The quasi‐maximum exponential likelihood estimators (QMELEs) of the model parameters are obtained, and their asymptotic properties are established. Simulation studies imply that the estimators are asymptotically normally distributed. An empirical investigation of stock returns illustrates our findings. Both the simulations and the example indicate that the QMELE is feasible, reliable and appropriate to fit the financial time series data of the Hang Seng Index.

A Time-Varying Coefficient Double Threshold GARCH Model with Explanatory Variables

“…For Lemma 2, by letting ω t ≡ 1 in Lemmas 2.2 and 2.3 of [36], we can directly obtain Lemma 2.2. The detailed proofs of Lemma A2, Lemma 3, Theorem 1 and Theorem 2 can be found in the appendix of [41], and, hence, we omit the proofs of these lemmas and theorems.…”

“…However, we do not use the LAD method to estimate the parameters of our model. Remark 2.2 in [41] gives a detailed description, and thus we will not consider the LAD method henceforward.…”

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.…”