How the Prediction Accuracy of Chaotic Time Series Depends on Methods of Determining the Parameters of Delay Vectors

• Autorzy: Witold Orzeszko
• Języki publikacji: EN

Abstrakty

EN

Unlike truly random processes, chaotic dynamics can be forecasted very precisely in a short run. In this paper, one of the methods applied to predicting chaotic dynamics - a local polynomial approximation, has been presented. A first step of this method is a reconstruction of system states by considering delay vectors. This procedure requires determining two parameters: an embedding dimension and a time delay. Examples of the methods developed for this purpose are false nearest neighbours and mutual information. The aim of this paper is to examine an adequacy of these techniques in application to forecast methods. In addition, an alternative method of determining the parameters of delay vectors is proposed.(fragment of text)

Słowa kluczowe

EN

Chaos theory; Time-series; Forecasting; Forecasting methods

PL

Teoria chaosu; Szeregi czasowe; Prognozowanie; Metody prognozowania

• Czasopismo: Dynamic Econometric Models
• Rocznik: 2004
• Tom: 6
• Strony: 231--239

Twórcy

autor

Witold Orzeszko

• Nicolaus Copernicus University in Toruń, Poland

Bibliografia

• Bask, M. (1998), Esseys on Exchange Rates: Deterministic Chaos and Technical Analysis, Working paper, Umea University, 1-36.
• Castagli, M. (1991), Eubank S., Farmer J. D., Gibson J., State Space Reconstruction in the Presence of Noise, Physica D, 51, 52-98.
• Casdagli, M. (1992), Chaos and Deterministic versus Stochastic Non-linear Modelling, Journal of the Royal Statistical Society B, 54, no. 2, 303-328.
• Farmer, J. D., Sidorowich, J. J. (1987), Predicting Chaotic Time Series, Physical Review Letters, 59, 845-848.
• Fraser, A. M., Swinney, H. L. (1986), Independent Coordinates for Strange Attractors from Mutual Information, Physical Review A, 33, 1134-1140.
• Kennel, M. B., Brown, R., Abarbanel, H. D. I. (1992), Determining Embedding Dimension for Phase-space Reconstruction Using a Geometrical Construction, Physical Review A, vol. 45, no. 6, 3403-3411.
• Lorenz, H-W. (1989), Nonlinear Dynamical Economics and Chaotic Motion, Springer-Verlag, Berlin Heidelberg.
• Łażewski, M., Zator, K. (2002), Analiza chaosu deterministycznego w szeregach czasowych cen akcji pozbawionych trendu a prognozowanie rynków finansowych (Analysis of Chaos in Detrended Stock Price Series and Prediction of Financial Data), in: Rynek kapitałowy. Skuteczne inwestowanie. (Capital market. Efficient investing), ed. W. Tarczyński, Szczecin, 333-344.
• Sordi S. (1996), Chaos in Macrodynamics: an Excursion Through the Literature, presented at Perspectives in Macroeconomics 12-13 04, 1-27.
• Takens, F. (1981), Detecting Strange Attractors in Turbulence, (D. Rand and L.Young, Eds), in: Dynamical Systems and Turbulence, Springer-Verlag, 366-381.
• Zawadzki, H. (1996), Chaotyczne systemy dynamiczne (Chaotic Dynamic Systems), Wydawnictwo Akademii Ekonomicznej im. Karola Adamieckiego, Katowice.
• Zeng, X., Pielke, R. A., Eykholt, R. (1992), Extracting Lyapunov Exponents From Short Time Series of Low Precision, Modern Physics Letters B, 6, 55-75.