This study explored the chaotic properties of human emotions as expressed in social media and its implications for attainable forecasting horizons. Three human emotional states extracted from Twitter were analyzed using the nonlinear dynamics approach. The greatest positive Lyapunov exponent (LE) and 0-1 test methods were applied to a time series set consisting of over 25,000 data points reflecting the hourly recorded data of over 1.3 million tweets. The results suggest that the examined emotional time series data represent a nonlinear dynamical system with deterministic chaos properties. Therefore, by utilizing traditional linear methods of social media data analysis, one may not be able to fully understand and forecast critical transition trends over time or beyond a limited duration. It was concluded that the nonlinear dynamics approach is useful to determine a feasible forecasting horizon and to assess the prediction accuracy of social media data in general.