GARCH Estimation and Discrete Stock Prices

The continuous-state GARCH model is misspecified if applied to returns calculated from discrete price series. This paper proposes modifications of the above model for handling such cases. The focus is on the AR-GARCH framework, but the same ideas could be used for other stochastic processes as well. Using Swedish stock price data and a stochastic optimization algorithm, simulated annealing, I compare the parameter estimates and asymptotic standard errors from the approximative model and the extended models. I find small deviations between the models for longer time series and small tick sizes, but larger differences for shorter series and for larger tick size to price ratios, mainly in the conditional variance parameter estimates. None of the models provide continuous residuals. By constructing generalized residuals, I show how valid residual diagnostic and specification tests can be performed in some cases.