Estimation of log-GARCH models in the presence of zero returns Articles uri icon

publication date

  • January 2018

start page

  • 809

end page

  • 827


  • 24

International Standard Serial Number (ISSN)

  • 1351-847X

Electronic International Standard Serial Number (EISSN)

  • 1466-4364


  • 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.


  • arch; exponential garch; log-garch; arma; inliers; missing values.