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Unbiased QML Estimation of LogGARCH Models in the Presence of Zero Errors
, 2013
"... A critique that has been directed towards the logGARCH model is that its logvolatility 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) nonzero value. However, this renders Quasi Maximum Likelihood (QML) ..."
Abstract

Cited by 2 (2 self)
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A critique that has been directed towards the logGARCH model is that its logvolatility 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) nonzero 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 Expectationmaximisation (EM) algorithm. Monte Carlo simulations confirm that the solution corrects the bias, and several empirical applications illustrate that the biascorrecting estimator can make a substantial difference. JEL Classification: C22, C58
An Exponential ChiSquared QMLE for LogGARCH Models Via the ARMA Representation∗
, 2013
"... Estimation of logGARCH 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 Chisquared QMLE for logGARCH models via the ARMA representation. The advantage of the estimator is that it co ..."
Abstract

Cited by 2 (2 self)
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Estimation of logGARCH 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 Chisquared QMLE for logGARCH 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 logGARCH 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 logGARCH(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. JEL Classification: C13, C22, C58
Unbiased Estimation of LogGARCH Models in the Presence of Zero Returns 1
, 2014
"... A critique that has been directed towards the logGARCH model is that its logvolatility 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) nonzero value. However, this renders estimation asymptotically bias ..."
Abstract
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A critique that has been directed towards the logGARCH model is that its logvolatility 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) nonzero value. However, this renders estimation asymptotically biased. Here, we propose a solution to the case where the true return is equal to zero with probability zero. In this case zero returns may be observed because of nontrading, measurement error (e.g. due to rounding), missing values and other data issues. The solution we propose treats the zeros as missing values and handles these by combining estimation via the ARMA representation with an ExpectationMaximisation (EM) type algorithm. An extensive number of simulations confirm the conjectured asymptotic properties of the biascorrecting algorithm, and several empirical applications illustrate that it can make a substantial difference in practice. JEL Classification: C22, C58