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The Generalised Autocovariance Function

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  • Tommaso, Proietti
  • Alessandra, Luati

Abstract

The generalised autocovariance function is defined for a stationary stochastic process as the inverse Fourier transform of the power transformation of the spectral density function. Depending on the value of the transformation parameter, this function nests the inverse and the traditional autocovariance functions. A frequency domain non-parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived. The results are employed to construct classes of tests of the white noise hypothesis, for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43711.

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Date of creation: 06 Jun 2012
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Handle: RePEc:pra:mprapa:43711

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Keywords: Stationary Gaussian processes. Non-parametric spectral estimation. White noise tests. Feature matching. Discriminant Analysis;

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  1. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
  2. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution free goodness-of-fit tests for linear processes," LSE Research Online Documents on Economics 6840, London School of Economics and Political Science, LSE Library.
  3. Tieslau, Margie A. & Schmidt, Peter & Baillie, Richard T., 1996. "A minimum distance estimator for long-memory processes," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 249-264.
  4. Steven N. Durlauf, 1992. "Spectral Based Testing of the Martingale Hypothesis," NBER Technical Working Papers 0090, National Bureau of Economic Research, Inc.
  5. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
  6. Ahmed El Ghini & Christian Francq, 2006. "Asymptotic Relative Efficiency of Goodness-Of-Fit Tests Based on Inverse and Ordinary Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 843-855, November.
  7. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
  8. Luati, Alessandra & Proietti, Tommaso & Reale, Marco, 2011. "The Variance Profile," MPRA Paper 30378, University Library of Munich, Germany.
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Cited by:
  1. Tommaso Proietti & Alessandra Luati, 2013. "Generalised Linear Spectral Models," CEIS Research Paper 290, Tor Vergata University, CEIS, revised 03 Oct 2013.
  2. Proietti, Tommaso & Luati, Alessandra, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," MPRA Paper 45280, University Library of Munich, Germany.

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