Financial data, such as daily or monthly maximum log return of stock price usually possess heavy tail and skewness properties. In this thesis, we consider stock price data of computer hardware and money center banks. Heavy-tailed distributions including Pearson type IV, Pearson type VII and stable distribution were fitted to the daily log return of the data sets, and goodness of fit were compared. For the monthly maximum log return, nonlinear threshold time series models were fitted with heavy tailed innovation distributions. In addition, the value at risk and volatility of the data sets are derived from the fitted distributions.