In this talk, we consider an entropy based goodness of fit (gof) test for iid random samples and autoregressive time series models with unit roots. For the iid case, special attention is made on discrete random variables. In order to deal with composite hypothesis tests,we consider the Khmaladze transformation method of the empirical process to remove the parameter estimation effect. This approach is applied to the construction of the entropy test whose limiting null distribution is free from the choice of paramter estimators.