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amplitude amplitude-modulated analysis approximate separability assume asymptotic separability average triple behaviour bootstrap change-point characteristic polynomial coefficients column confidence intervals corresponding decomposition defined denote depicted in Fig described diagonal averaging Double centring eigentriple rearrangement eigenvalues eigenvectors equal example extraction Figure finite forecasting algorithm frequencies H-matrix Hankel Hankel matrix harmonic components harmonic series heterogeneity matrix homogeneous initial series inner product integer L-continuation L-lagged lagged vectors leading eigentriples linear space min(L minimal LRF nonzero obtain original series orthogonal orthonormal orthonormal basis parameters periodogram problem Proposition reconstructed series recurrent continuation recurrent forecasting residual series row detection function Section series components series F series F(1 series F/v signal singular value decomposition singular values singular vectors span spectral measure stable separability stationary series strong separability structure Theorem thick line thin line tion Toeplitz trajectory matrix trend vector forecasting weak separability white noise window length zero
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