ZD-GARCH model: a new way to study heteroscedasticity

Dong Li, Shiqing Ling and Ke Zhu

MPRA Paper from University Library of Munich, Germany

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

Keywords: Conditional heteroscedasticity; GARCH model; Generalized quasi-maximum likelihood estimator; Heteroscedasticity; Portmanteau test; Stability test; Top Lyapunov exponent; Zero-drift GARCH model. (search for similar items in EconPapers)
JEL-codes: C0 C01 C5 C51 (search for similar items in EconPapers)
Date: 2016-01-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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