Estimation of log-GARCH models in the presence of zero returns
针对零收益导致对数GARCH模型无法估计的问题，提出将零视为缺失值并通过ARMA表示进行估计的算法，模拟和实证表明该算法能有效纠正偏差。
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 if the true return is equal to zero with probability zero. Here, we propose a solution. If the zero probability is zero, then 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 properties of the bias-correcting algorithm, and several empirical applications illustrate that it can make a substantial difference in practice.