Abstract

Deriving a relationship that allows to predict future values of a time series is a challenging task when the underlying law is highly non linear. Usually, when facing with a problem of non-linear prediction, we are provided with the past history of the time series and we want to extract from that set of data a mathematical function that relates a certain window of past values with the value T time steps ahead in the future. In practical problems the discovering of a forecasting function is hard since we deal with processes corrupted by noise due to an inaccurate modeling of the system and to the measurement procedure. Another important characteristic of the signal that has to be considered is its stationarety. An adaptive forecasting technique should be devised for non-stationary processes. This is particularly true for the analysis and for all the attempts in forecasting financial time series. It seems that such series are intrinsecally non stationary and that a complete model requires not only the knowledge of past values of the series but also some other information regarding the environment. The results in this field are contradictory but it is clear that trying to infer a global unchanging model from the historical information leads to results comparable with a random walk [8]. We try to use a different approach for prediction rather than dynamical system modeling that is usually the basis for time series characterization. We transform the prediction problem in a classification task and we use a statistical approach based on the k-nearest neighbors algorithm to obtain the most probable variation with respect to the present price value. Index terms: Nearest-neighbors, Financial time series.

Citations