Over the last years the demand for new economic and mathematical tool formation has appeared for both analysis of economical dynamics and a strategy generation of economic process management. Methods used before are not effective any more, the crises and standard of well-being decrease stemmed from it. Many economic systems are characterized by long-term memory. That is the behavior of the system is defined not only by the set of parameters at the exact moment but also by time history at previous moments. Thus, in this connection, there should be some quantitative methods enabling to disclose the dynamics of the processes at the market, factors that influence on market rates formation. This book, therefore, provides a wide variety of methods of dynamic system state estimation. The method for estimating dynamic systems in the case of measured output and the speed of its changing has been developed and optimized. The theoretical data of the paper can find an application to any dynamic system, in particular to any sphere of economy.