The world went through weeks of financial turbulence in stock markets and investors were overcome by fears fuelled by more bad news, while countries continued their attempts to calm the markets with more injection of funds. By these very disturbed times, even if traders hope extreme risk aversion has passed, an investor would like predict the future of the market in order to protect his portfolio and a speculator would like to optimize his tradings. This thesis describes the design of numerical models and algorithms for the forecasting of financial time series, for speculation on a short time interval. To this aim, we will use two models: - " Price Forecasting Model " forecasts the behavior of an asset for an interval of three hours. This model is based on Functional Clustering and smoothing by cubic-splines in the training phase to build local Neural models, and Functional Classification for generalization, - " Model of Trading " forecasts the First Stopping time, when an asset crosses for the first time a threshold defined by the trader. This model combines a Price Forecasting Model for the prediction of market trend, and a Trading Recommendation for prediction of the first stopping time. We use an auto-adaptive Dynamic State Space Model, with Particle Filters and Kalman-Bucy Filters for parameter estimation.