- Tytuł:
- Wavelets for time series analysis - a survey and new results
- Autorzy:
-
Mielniczuk, J.
Wojdyłło, P. - Powiązania:
- https://bibliotekanauki.pl/articles/970989.pdf
- Data publikacji:
- 2005
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
long-range dependence
decorrelation property
spectral density
time series
wavelets
fractional Gaussian noise (FGN)
fractional autoregressive integrated moving average (FARIMA)
Hurst exponent
falka - Opis:
- 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.
- Źródło:
-
Control and Cybernetics; 2005, 34, 4; 1093-1125
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł