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2007 | nr 1153 | 339
Tytuł artykułu

Nieliniowa dynamika szeregów czasowych w badaniach ekonomicznych

Autorzy
Warianty tytułu
Nonlinear Dynamics of the Economic Time Series Data
Języki publikacji
PL
Abstrakty
Zaprezentowano krótkie wprowadzenie do analizy układów dynamicznych i teorii chaosu deterministycznego. Przedstawiono dokonania nauki w zakresie stosowania narzędzi analizy nieliniowej i teorii chaosu deterministycznego do badań praktycznych. Zaprezentowano wybrane aspekty modelowania układów dynamicznych. Omówiono problemy przygotowania danych ekonomicznych i wstępnej ich analizy. Przedstawiono teorie i praktyczne algorytmy obliczania wymiarów układów dynamicznych, wykładników Lapunowa oraz różnych typów entropii. Zaprezentowano metody badania samopodobieństwa procesów dynamicznych oraz wizualne metody analizy ekonomicznych szeregów czasowych. Przedstawiono konkretne testy nieliniowości i chaosu, a także tzw. metodę danych zastępczych w analizie nieliniowej szeregów czasowych.
EN
Nonlinearity and chaos are two terms, which in the last years of the twentieth century practically dominated many areas dealing with quantitative description of the surrounding reality. The nonlinear world means that result is not directly dependent and proportional to the obvious cause, and more and more often we realize that we are living in such a world. Nonlinearity means also that mathematical analysis and description of some dynamical processes become really difficult. This results in occurrence of some processes' special behaviour, which seems to us as not possible to be explained by the theory of the deterministic dynamics. The evident existence of some chaotic phenomena is often caused by specific nonlinear dynamic systems properties, for example particular sensitivity of system behaviour to very small changes of initial conditions. These changes can be exponentially magnified on some chaotic system trajectories, resulting in practical impossibility of the future dynamic system behaviour forecasting. The contemporary way of understanding chaos and its presence in nature is not equivalent with the total inability of understanding the origin dependencies in studied processes, but caused by the difficulties of establishing these initial conditions and precisely measuring their changes. Very important is the observation that seemingly very simple deterministic systems can be characterized by dynamics very complicated, complex and similar to random. So the substantial amount of recent research has sought to elucidate the role of nonlinearity and chaos in economic processes that often behave in similar way. Some of the work has been theoretical, attempting to ascertain whether simple nonlinear deterministic models can exhibit the kind of fluctuations typically found in economic data. Other work has been empirical, and discusses the possibility that actual economic time series are characterized by chaotic dynamics. Both types of research are regarded as being rather in the early stages and none of these developments is far enough along to bring the change in the way economic practitioners proceed. Nevertheless, the fact that so much research is being done suggests that we can expect new and important policy implications from this approach. This book surveys the recent research and attempts to present a picture of potential nonlinearity and deterministic chaos economic implications. In doing so, focus is placed first on the ways and problems of nonlinear, dynamic systems reconstruction based on the economic time series data. Secondly, we concentrate on the efficacy of determinism and nonlinearity tested in economic processes in the case where only time series data are available. The main goal of the book was the thorough demonstration of practical nonlinear analysis methods and the ways of detection of the deterministic chaos possible existence. The presented methods are supplied with description of the using rules, specific requirements for numeric applications, problems of data preprocessing, practical counting procedures and indication of troubles with understanding of the obtained findings. Inside one can also find some numerical results for real economic time series data with addition of the consequent interpretations. The book consists of the introduction, nine subject chapters and a special supplement with descriptions of used mathematical symbols and abbreviations, short lexicon of main terms connected with nonlinear analysis and chaos theory and the listing of references. The first chapter includes the basics of nonlinear and chaotic dynamics theory; the second presents the existing publications on using this theory in the field of economy. The third chapter indicates some problems connected with the reconstruction of dynamic systems generating examined unidimensional observation sequences. Some next chapters are crucial for the book, presenting real tests for determinism, nonlinearity and chaos. In detail we can mention here problems with data preprocessing and testing their stationarity. The chapter 5 describes the theory and numerical algorithms for dimensions, entropies and Lyapunov exponents, which can characterize stochastic-deterministic dynamic processes. Some next chapters concern for examining self-similarity and visual analysis of dynamic processes based on their topological properties. The last chapters present some tests for nonlinearity and chaos, as well as testing statistical hypotheses of the certain distribution properties of analyzed time series with new methods of generating the surrogate data. Besides, almost all chapters include results of the wide range of the comparative tests for selected economic time series and seemingly similar random and chaotic dynamic processes. (original abstract)
Twórcy
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