Estimation of Log-GARCH Models in the Presence of Zero Returns

A 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 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 non-trading, measurement error (e.g. due to rounding), missing values and other data issues. The algorithm we propose treats the zeros as missing values and handles these by estimation via the ARMA representation. An extensive number of simulations verify the conjectured asymptotic properties of the bias-correcting algorithm, and several empirical applications illustrate that it can make a substantial difference in practice.