We present a method to compensate statistical errors in the calculation of correlations on asynchronous time series. The method is based on the assumption of an underlying time series. We set up a model and apply it to financial data to examine the decrease of calculated correlations towards smaller return intervals (Epps effect). We show that this statistical effect is a major cause of the Epps effect. Hence, we are able to quantify and to compensate it using only trading prices and trading times.