Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns
AbstractA critique that has been directed towards the log-GARCH model is that its log-volatility specification does not exist in the presence of zero returns. A common ``remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders Quasi Maximum Likelihood (QML) estimation asymptotically biased. Here, we propose a solution to the case where actual returns are equal to zero with probability zero, but zeros nevertheless are observed because of measurement error (due to missing values, discreteness approximisation error, etc.). The solution treats zeros as missing values and handles these by combining QML estimation via the ARMA representation with the Expectation-maximisation (EM) algorithm. Monte Carlo simulations confirm that the solution corrects the bias, and several empirical applications illustrate that the bias-correcting estimator can make a substantial difference.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 50699.
Date of creation: 09 Sep 2013
Date of revision:
ARCH; exponential GARCH; log-GARCH; ARMA; Expectation-Maximisation (EM);
Other versions of this item:
- Genaro Sucarrat & Álvaro Escribano, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," Economics Working Papers we1321, Universidad Carlos III, Departamento de Economía.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-10-25 (All new papers)
- NEP-ECM-2013-10-25 (Econometrics)
- NEP-ETS-2013-10-25 (Econometric Time Series)
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