Financial returns are often modelled as autoregressive time series with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes have been intensely studying in financial and econometric literature as risk models of many financial time series. Analyzing two data sets of stock prices we try to fit AR(1) processes with GARCH or EGARCH errors to the log returns. Moreover, hyperbolic or generalized error distributions occur to be good models of white noise distributions.