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Identification of Persistent Cycles in Non‐Gaussian Long‐Memory Time Series
Author(s) -
Boutahar Mohamed
Publication year - 2008
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.1467-9892.2008.00576.x
Subject(s) - mathematics , central limit theorem , autoregressive model , asymptotic distribution , unit circle , limit (mathematics) , sequence (biology) , gaussian , polynomial , series (stratigraphy) , gaussian process , distribution (mathematics) , stable distribution , mathematical analysis , statistics , estimator , paleontology , physics , quantum mechanics , biology , genetics
. Asymptotic distribution is derived for the least squares estimates (LSE) in the unstable AR( p ) process driven by a non‐Gaussian long‐memory disturbance. The characteristic polynomial of the autoregressive process is assumed to have pairs of complex roots on the unit circle. In order to describe the limiting distribution of the LSE, two limit theorems involving long‐memory processes are established in this article. The first theorem gives the limiting distribution of the weighted sum,is a non‐Gaussian long‐memory moving‐average process and ( c n , k ,1 ≤ k ≤ n ) is a given sequence of weights; the second theorem is a functional central limit theorem for the sine and cosine Fourier transforms