An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation

Francq, Christian and Sucarrat, Genaro (2013): An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation.

Abstract

Estimation of log-GARCH models via the ARMA representation is attractive because it enables a vast amount of already established results in the ARMA literature. We propose an exponential Chi-squared QMLE for log-GARCH models via the ARMA representation. The advantage of the estimator is that it corresponds to the theoretically and empirically important case where the conditional error of the log-GARCH model is normal. We prove the consistency and asymptotic normality of the estimator, and show that, asymptotically, it is as efficient as the standard QMLE in the log-GARCH(1,1) case. We also verify and study our results in finite samples by Monte Carlo simulations. An empirical application illustrates the versatility and usefulness of the estimator.

• Item Type: MPRA Paper
• Language: English
• Keywords: Log-GARCH, EGARCH, Quasi Maximum Likelihood, Exponential Chi- Squared, ARMA
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

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