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Identification of Persistent Cycles in Non‐Gaussian Long‐Memory Time Series

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  • Mohamed Boutahar

Abstract

. 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 (cn,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

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  • Mohamed Boutahar, 2008. "Identification of Persistent Cycles in Non‐Gaussian Long‐Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 653-672, July.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:4:p:653-672
    DOI: 10.1111/j.1467-9892.2008.00576.x
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    1. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
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    1. McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.

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