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Author
Bereś Helena, Bereś Krzysztof, Zięba Jolanta
Title
Metody wyznaczania współczynnika Hursta dla procesów telekomunikacyjnych i bankowych
Methods of Calculating the Local Hurst Parameter for Telecommunication and Bank Processes
Source
Bank i Kredyt, 2004, nr 4, s. 41-47
Keyword
Telekomunikacja, Bankowość, Procesy stochastyczne, Metody statystyczne, Rozkład Pareta
Telecommunication, Banking, Stochastic processes, Statistical methods, Pareto distribution
Note
summ.
Abstract
Podjęto próbę wyznaczenia zależności funkcji samopodobieństwa w procesach telekomunikacyjnych oraz w niektórych procesach bankowych. Przeanalizowano dwa przykłady procesów bankowych. Pierwszy to rozkład dziennych kwotowań stóp procentowych rynku pieniężnego WIB. W drugim dokonano analizy wahań poziomu środków pieniężnych utrzymywanych przez banki komercyjne na rachunkach bieżących w NBP, w odniesieniu do średniego poziomu rezerwy obowiązkowej, który zależy od stopy rezerw ustalanej przez NBP.

In the paper the authors assume that observed telecommunication and bank processes may be represented with the aid of time-dependent parameters. Since these parameters sometimes change very rapidly, the wavelet transform was used to identify them. The paper begins with definitions of the stationary process, the self-similarity stationary process, and the Wang et al. dependence of local power spectra on local self-similarity Hurst parameter. After making calculations the authors have arrived at the following conclusions: 10 The telecommunication processes such as line occupation time or talking time in the study data have local Hurst parameter values in the range. This implies that these processes are self-similar and stationary. Independently of the above calculations the tails of the wavelet transform coefficients at the highest scale were approximated by a generalized Pareto distribution and indicated a shape parameter . This is in accordance with the previously calculated local Hurst parameter and suggests that the studied telecommunication process should be classified as self-similar stationary increment processes (type H-sssi). Unlike for the studied telecommunication processes, the Hurst parameters calculated for bank WIBOR data show that these processes are non-stationary. In the next part our paper generalized Pareto distributions are used to check whether the bank rate of WIBOR (Warsaw interbank deposit rates) consists of independent and identical distributed random variables (iid). The results of these calculations did not agree with the above presented hypothesis and showed that: 20 The set of WIBOR processes are dependent on one another. The authors suggest that this dependence may be due to the monetary authority decisions. In this situation values of shape parameter ? for each WIBOR level may be representative of the strength of the NBP reference rates influence on the money market situation. Calculations similar to the above were
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Bibliography
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  1. I. Daubechies (1992): Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia: SIAM.
  2. P. Embrechts, C, Klüppelberg, H. Mikosch (1997): Modeling of extremely events for insurance and finance. Springer-Verlag, Berlin, Heidelberg.
  3. M. Maejima (1986): A remark on self-similar processes with stationary increments. Canadian J. Statist. 14, s. 81-82.
  4. S.G. Mollat (1989): A Theory for Multi-Resolution Decomposition. IEEE, Trans. Pat. Mach. Intel. 11, s. 674-693.
  5. D.B. Percival, A.T. Walden (2000): Wavelet Methods for Time Series Analysis. Cambridge University Press.
  6. Y. Wang, J.E. Cavenaugh, C. Song (2001): Self-similarity index estimation via wavelets for locally self-similar processes. "Journal of Statistical Planning and Inference" 99, s. 91-110.
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ISSN
0137-5520
Language
pol
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