In this paper, the problem of estimating the current value of financial instruments using multidimensional statistical analysis is considered. The research considers various approaches to constructing regression computational schemes using quotes of financial instruments correlated to the data as regressors. An essential feature of the problem is the chaotic nature of its observation series, which is due to the instability of the probabilistic structure of the initial data. These conditions invalidate the constraints under which traditional statistical estimates remain non-biased and effective. Violation of experiment repeatability requirements obstructs the use of the conventional data averaging approach. In this case, numeric experiments become the main method for investigating the efficiency of forecasting and analysis algorithms of observation series. The empirical approach does not provide guaranteed results. However, it can be used to build sufficiently effective rational strategies for managing trading operations.
We consider the problem of evolutionary self-organization of control strategies using the example of speculative trading in a non-stationary immersion market environment. The main issue that obstructs obtaining real profit is the extremely high instability of the system component of observation series which implement stochastic chaos. In these conditions, traditional techniques for increasing the stability of control strategies are ineffective. In particular, the use of adaptive computational schemes is difficult due to the high volatility and non-stationarity of observation series. That leads to significant statistical errors of both kinds in the generated control decisions. An alternative approach based on the use of dynamic robustification technologies significantly reduces the effectiveness of the decisions. In the current work, we propose a method based on evolutionary modeling, which supplies structural and parametric self-organization of the control model.
This article considers a short-term forecasting of a process that is an output signal of a nonlinear system observed on the background of additive noise. Forecasting is made possible thanks to the technique of nonparametric estimation of local trends. The main problem in this case is the instability of the time of the existence of these local trends. The average duration of relatively stable intervals can be estimated from earlier observation history. Such approaches are called channel strategies. The task of constructing such strategies for EURUSD asset management in the conditions of market chaos is considered, as well as the potential capabilities of these management strategies via computational experiments. We demonstrated the fundamental possibility of achieving profit even for areas with complex dynamics with abrupt changes in the considered process. We propose improved channel strategies and also denote the main directions of increasing their effectiveness.
Predicting the state of a dynamic system influenced by a chaotic immersion environment is an extremely difficult task, in which the direct use of statistical extrapolation computational schemes is infeasible. This paper considers a version of precedent forecasting in which we use the aftereffects of retrospective observation segments that are similar to the current situation as a forecast. Furthermore, we employ the presence of relatively stable correlations between the parameters of the immersion environment as a regularizing factor. We pay special attention to the choice of similarity measures or distances used to find analog windows in arrays of retrospective multidimensional observations.
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