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

Mohamed Boutahar

Journal of Time Series Analysis, 2008, vol. 29, issue 4, 653-672

Abstract: 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

Date: 2008
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