Wpływ doboru metod wyznaczania parametrów rekonstrukcji przestrzeni stanów układu dynamicznego na dokładność prognoz

Forecasting economic phenomena is a complex issue which in recent decades some have approached using different statistical and econometric methods. There has recently been a huge increase in interest in the theory of non-linear dynamic systems. This has resulted in the emergence of new prediction methods that use the concepts and methods associated with non-linear dynamic systems. One of this theory’s main forecasting tools is the reconstruction of the state space of the dynamic system. It consists in approximately the original state space and dynamics of the system through the construction of multi-dimensional space only on the basis of observations of one variable. The most common reconstruction method is the method of delays, which can be employed to build a set of d variables using a one-dimensional time series xt. These variables are obtained by shifting “the original” time series about a fixed delay τ. The main goal of the article is to assess the quality of the forecasts obtained using (d, τ) parameters of the state space reconstruction of a dynamic system of designated methods: correlation integrals C – C, mutual information, an analysis of auto-correlation functions, and false nearest neighbours. The test will be conducted based on financial time series, which consist of the closing prices of shares of companies quoted on the Warsaw Stock Exchange and the daily exchange rates.