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ZD-GARCH model: a new way to study heteroscedasticity

Li, Dong and Ling, Shiqing and Zhu, Ke (2016): ZD-GARCH model: a new way to study heteroscedasticity.

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Abstract

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent $\gamma_{0}$ , but interestingly when $\gamma_{0}$ = 0, it is stable with its sample path oscillating randomly between zero and infinity over time. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of ZD-GARCH(1, 1) model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for $\gamma_{0}$, a test for stability, and a portmanteau test for model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) model is more appropriate to capture heteroscedasticity than a non-stationary GARCH(1, 1) model, which suffers from an inconsistent QMLE of the drift term

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