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Analysis of time series is very useful in science to realize modeling, filtering, prediction or smoothing. In the highly complex market structure the intra-day dealers are faced with different constraints and use different strategies to reach their financial goals such as maximizing their profits or utility function after adjusting for market risk. The procedures described in this book are suited for high frequency data showing nonlinear dependencies and observed at irregularly and randomly spaced times or when data are curves with different time points. Standard statistical methods completely fail in these cases. To overcome this problem we use functional analysis and neural networks. Often we have hidden variables that we cannot directly observe, or their measurement are costly or disturb the process. We can estimate these hidden variables, from measurement of other variables, using a Dynamic State Space Model with Kalman and Particle Filters. The methodologies and algorithms described in this book are suited for financial, engineering, physical applications when classical statistical methods fail.