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Wpływ redukcji szumu losowego metodą najbliższych sąsiadów na stabilność największego wykładnika Lapunowa w ekonomicznych szeregach czasowych

100%
Miśkiewicz-Nawrocka M.
Studia Ekonomiczne
|
2014
|
vol. 203
101-113
EN
The Oseledec theorem (1968) and the theorems given in the paper Eckmann, Ruelle (1985) show the Lyapunov exponents exist for almost all the points in the state space of a dynamical system, and they are constant for almost all points in the basin of attraction of the attractor of dynamical system. However, the above-mentioned theorem applies only to deterministic systems. The Oseledec theorem provides the stability of the largest Lyapunov exponent regardless of the number of observations for the time series generated by deterministic chaotic system. While for the time series generated by a stochastic system, increase the number of observations in a series will cause change in the value of the largest Lyapunov exponent. In this paper researched the effect of the number of observations of the time series on the value of largest Lyapunov exponent. In addition, the stability of the largest Lyapunov exponent was examined in the time series after random noise reduction procedure.
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Wpływ redukcji poziomu szumu losowego metodą najbliższych sąsiadów na dokładność prognoz finansowych szeregów czasowych

84%
Zeug-Żebro K.
Studia Ekonomiczne
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2013
|
vol. 146
111-118
EN
The real time series xt is usually disturbed by random noise. His source may be errors of measurement and errors of rounding made during data analysis. The random noise may also represent an exogenous factors affecting the dynamics of the system or be a consequence of the statistical nature of the phenomena, e.g. which are affected by human decisions. Since the presence of noise in the data can significantly affect the quality of the forecasts, the aim of the article will be to evaluate the accuracy of predicting the time series filtered using the method of nearest neighbors. The test will be conducted on the basis of the financial time series, which consist of closing prices of companies listed on the Warsaw Stock Exchange and the daily exchange rates.
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