Application of robust observers to time-series forecasting

Robust observers are frequently designed to estimate the states of a system that prohibit direct measurements. In this thesis we develop an efficient algorithm for designing an observer that provides robust estimation of higher-order derivatives of a continuous time-series. These estimations are subsequently used in the design of a novel procedure that offers a fairly accurate forecast of time-series on relatively short time-horizons. The dependence of forecast error upon the duration of the forecast-horizon is studied on several representative examples.