Time series analysis is used in numerous fields. Time series data is everywhere, from economics, statistics, biology, and beyond. Most often, we wish to make predictions or forecasts for future events. We would ultimately like to know what would happen in the future, given all the information seen in the past. Methods for analyzing forecasts and creating prediction intervals for linear time series analysis are well known. However, there is a need to develop methods to construct prediction intervals for non-linear time series. Non-linear time series data is generated from the Ro_ssler system, and the nonparametric method of thin plate splines is used to model the time series. This thesis examines the use, and presents the results of, forecasts and corresponding prediction intervals based on the stationary bootstrap.