摘要: We introduce the concept of local dyadic stationarity, to account for non-stationary time series, within framework Walsh-Fourier analysis. define and study varying ARMA models (tvDARMA). It is proven that general tvDARMA process can be approximated locally by either a tvDMA tvDAR process.
harvard.edu
arxiv.org参考文章(42)
Mohammad Maqusi, Applied Walsh analysis ,(1981)
Rainer Dahlhaus, A Likelihood Approximation for Locally Stationary Processes Annals of Statistics. ,vol. 28, pp. 1762- 1794 ,(2000) , 10.11588/HEIDOK.00020783
Maurice Priestley, Non-linear and non-stationary time series analysis ,(1988)
Rainer Dahlhaus, Locally Stationary Processes arXiv: Statistics Theory. ,vol. 30, pp. 351- 413 ,(2012) , 10.1016/B978-0-444-53858-1.00013-2
Hernando Ombao, Jonathan Raz, Rainer von Sachs, Wensheng Guo, The SLEX model of a non-stationary random process Annals of the Institute of Statistical Mathematics. ,vol. 54, pp. 171- 200 ,(2002) , 10.1023/A:1016130108440
Ralph Selfridge, Generalized Walsh transforms. Pacific Journal of Mathematics. ,vol. 5, pp. 451- 480 ,(1955) , 10.2140/PJM.1955.5.451
Takeaki Nagai, Masanobu Taniguchi, Walsh spectral analysis of multiple dyadic stationary processes and its applications Stochastic Processes and their Applications. ,vol. 24, pp. 19- 30 ,(1987) , 10.1016/0304-4149(87)90025-1
Michael H. Neumann, Rainer von Sachs, Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra Annals of Statistics. ,vol. 25, pp. 38- 76 ,(1997) , 10.1214/AOS/1034276621
R. Dahlhaus, Fitting time series models to nonstationary processes Annals of Statistics. ,vol. 25, pp. 1- 37 ,(1997) , 10.1214/AOS/1034276620
M. Taniguchi, L. C. Zhao, P. R. Krishnaiah, Z. D. Bai, Statistical analysis of dyadic stationary processes Annals of the Institute of Statistical Mathematics. ,vol. 41, pp. 205- 225 ,(1989) , 10.1007/BF00049392