Using a normal distribution as the assumed probability generating process is only appropriate if the underlying data follow a normally distributed process. Most financial and economic time series exhibit substantial deviations from normally distributed processes. Note that maximum likelihood estimators select values for model parameters that maximize the likelihood that observed data will occur in a sample. The maximum likelihood method can be used with any type of probability distribution. Mean reversion characteristics of parameters would not be considered a shortcoming for using the normal distribution. | 
