This short article is concerned with a categorical time series obtained after clipping a heteroscedastic GARCH process. Estimation methods are discussed for the model parameters appearing both in the original process and in the resulting binary time series from a clipping (cf. Zhen and Basawa, 2009). Assuming AR-GARCH model for heteroscedastic time series, three data sets from Korean stock market are analyzed and illustrated with applications to calculating certain probabilities associated with the AR-GARCH process.