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    Sela, Rebecca J. and Hurvich, Clifford M. 2012. The averaged periodogram estimator for a power law in coherency. Journal of Time Series Analysis, Vol. 33, Issue. 2, p. 340.

    Hidalgo, J. and Yajima, Y. 2003. Semiparametric estimation of the long-range parameter. Annals of the Institute of Statistical Mathematics, Vol. 55, Issue. 4, p. 705.

    Velasco, Carlos 2003. Nonparametric frequency domain analysis of nonstationary multivariate time series. Journal of Statistical Planning and Inference, Vol. 116, Issue. 1, p. 209.


Spectral Analysis for Bivariate Time Series with Long Memory

  • J. Hidalgo (a1)
  • DOI:
  • Published online: 01 February 2009

This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time series, continue to hold for long memory processes when λ lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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