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A CENTRAL LIMIT THEOREM OF FOURIER TRANSFORMS OF STRONGLY DEPENDENT STATIONARY PROCESSES
Author(s) -
Yajima Yoshihiro
Publication year - 1989
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1989.tb00036.x
Subject(s) - mathematics , central limit theorem , autoregressive model , fourier transform , stationary process , fourier series , mathematical analysis , limiting , fourier analysis , stable process , limit (mathematics) , discrete fourier transform (general) , stable distribution , statistical physics , fractional fourier transform , stochastic process , statistics , physics , mechanical engineering , engineering
. We consider a limiting distribution of the finite Fourier transforms of observations drawn from a strongly dependent stationary process. It is proved that the finite Fourier transforms at different frequencies are asymptotically independent and normally distributed. Our result can apply to a fractional autoregressive integrated moving‐average process and a fractional Gaussian noise, two examples of strongly dependent stationary processes.