Metoda danych zastępczych w analizie nieliniowej szeregów czasowych - Nowiński, Marek; Masłowski, Michał (Surrogate Data Method in Nonlinear Time Series Analysis, 2007)
The main goal of nonlinear time series analysis is to detect important, but other than linear, properties of scalar observations generated by deterministic, dynamic systems, including these affected by noise. But before applying nonlinear techniques to dynamical phenomena occurring in a real-world environment, it is necessary to ask if the use of such advanced techniques is justified by specific pattern in the data. While many processes in nature a priori seem very unlikely to be linear, the possible nonlinear nature might not be evident in their dynamics. The method of surrogate data gives us possibility to answer this question. The analysis should enable identification of deterministic nonlinear dependencies in data and possibly chaotic character of the process. One of the most important tasks is to evaluate topological invariants of the reconstructed system, which is helpful in determining its nonlinear properties. The breakthrough was made with the idea of using the surrogate data method for testing hypotheses about the form of dependencies appearing in analyzed data. This method uses specific discriminating statistics to the raw and surrogate data in order to reject possibilities that original time series data are the result of some linear stochastic process of specific kind. But if we want statistically rigorous and foolproof method, we should show some real limitations and caveats that appear in its practical use. This is the aim of this paper, together with presenting the range of tested hypotheses, discriminating statistics and algorithms generating surrogate data. The practical results of application of the surrogate data method to real economic time series are also presented.
Prace Naukowe Akademii Ekonomicznej we Wrocławiu; 2007; nr 1167, s. 180-194