Nonparametric Estimation for Locally Stationary GARCH Processes with Laplace-Distributed Noise
Abstract
This paper investigates the Quasi-Maximum Likelihood Estimation (QMLE) method for time-varying GARCH models under the assumption that the innovations follow the standard Laplace distribution. We consider a locally stationary framework. The estimation process is based on a kernel-weighted likelihood approach. We establish the consistency and asymptotic normality of the proposed estimators under regularity assumptions. The efficacy of the method is demonstrated through simulation studies and an application to real-world financial data, highlighting the practical advantages of modeling heavy-tailed innovations with the Laplace distribution.
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