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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.

Suggested Citation

  • Tommaso, Proietti & Alessandra, Luati, 2012. "The Generalised Autocovariance Function," MPRA Paper 43711, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:43711
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Alessandra Luati & Francesca Papagni & Tommaso Proietti, 2021. "Efficient Nonparametric Estimation of Generalized Autocovariances," CEIS Research Paper 515, Tor Vergata University, CEIS, revised 14 Oct 2021.
    3. Caporin, Massimiliano & Costola, Michele, 2022. "Time-varying Granger causality tests in the energy markets: A study on the DCC-MGARCH Hong test," Energy Economics, Elsevier, vol. 111(C).
    4. Tommaso Proietti & Alessandra Luati, 2013. "Generalised Linear Spectral Models," CEIS Research Paper 290, Tor Vergata University, CEIS, revised 03 Oct 2013.

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    More about this item

    Keywords

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

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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