Wavelets for time series analysis - a survey and new results

• Autorzy: Mielniczuk J. , Wojdyłło P.
• Języki publikacji: EN

Abstrakty

EN

In the paper we review stochastic properties of wavelet coefficients for time series indexed by continuous or discrete time. The main emphasis is on decorrelation property and its implications for data analysis. Some new properties are developed as the rates of correlation decay for the wavelet coefficients in the case of long-range dependent processes such as the fractional Gaussian noise and the fractional autoregressive integrated moving average processes. It is proved that for such processes the within-scale covariance of the wavelet coefficients at lag k is O(k^2(H-N)-2), where H is the Hurst exponent and N is the number of vanishing moments of the wavelet employed. Some applications of decorrelation property are briefly discussed.

Słowa kluczowe

EN

decorrelation property; spectral density; time series; wavelets; fractional Gaussian noise (FGN); fractional autoregressive integrated moving average (FARIMA); Hurst exponent; long-range dependence

PL

falka

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2005
• Tom: Vol. 34, no 4
• Strony: 1093--1125
• Opis fizyczny: Bibliogr. 35 poz., wykr.

Twórcy

autor

Mielniczuk J.

• Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warsaw, Poland

autor

Wojdyłło P.

• Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warsaw, Poland

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