Title of article :
Law of the iterated logarithm for the periodogram
Author/Authors :
Cuny، نويسنده , , Christophe and Merlevède، نويسنده , , Florence and Peligrad، نويسنده , , Magda، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
Abstract :
We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density function associated with the stationary process. Results for a specified frequency are also given. Our results also lead to the law of the iterated logarithm for the real and imaginary parts of the discrete Fourier transform. The proofs rely on martingale approximations combined with results from harmonic analysis and techniques from ergodic theory. Several applications to linear processes and their functionals, iterated random functions, mixing structures and Markov chains are also presented.
Keywords :
Periodogram , Spectral Analysis , Law of the iterated logarithm , Martingale approximation , Discrete Fourier Transform
Journal title :
Stochastic Processes and their Applications
Journal title :
Stochastic Processes and their Applications