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The generalised autocovariance function

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  • Proietti, Tommaso
  • Luati, Alessandra

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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  • Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:1:p:245-257
    DOI: 10.1016/j.jeconom.2014.07.004
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    1. Christian Francq & Jean‐Michel Zakoïan, 2009. "Bartlett's formula for a general class of nonlinear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 449-465, July.
    2. Francesco Battaglia, 1983. "Inverse Autocovariances And A Measure Of Linear Determinism For A Stationary Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(2), pages 79-87, March.
    3. Alessandra Luati & Tommaso Proietti & Marco Reale, 2012. "The Variance Profile," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 607-621, June.
    4. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(2), pages 382-416, April.
    5. R. J. Bhansali, 1993. "Estimation Of The Prediction Error Variance And An R2 Measure By Autoregressive Model Fitting," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(2), pages 125-146, March.
    6. Francesco Battaglia, 1988. "On The Estimation Of The Inverse Correlation Function," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(1), pages 1-10, January.
    7. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    8. 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 231-247, July-Sept.
    9. Willa W. Chen & Rohit S. Deo, 2004. "Power transformations to induce normality and their applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 117-130, February.
    10. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    11. Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December.
    12. Velasco, Carlos, 2000. "Non-Gaussian Log-Periodogram Regression," Econometric Theory, Cambridge University Press, vol. 16(1), pages 44-79, February.
    13. 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.
    14. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
    15. A. T. Walden, 1994. "Interpretation of Geophysical Borehole Data Via Interpolation of Fractionally Differenced White Noise," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 335-345, June.
    16. Chen Zhao‐Guo & E. J. Hannan, 1980. "The Distribution Of Periodogram Ordinates," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 73-82, January.
    17. Delgado, Miguel A. & Hidalgo, Javier & Velasco, Carlos, 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.
    18. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    19. 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.
    20. Fay, Gilles & Soulier, Philippe, 2001. "The periodogram of an i.i.d. sequence," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 315-343, April.
    21. Gilles Fay & Eric Moulines & Philippe Soulier, 2002. "Nonlinear functionals of the periodogram," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(5), pages 523-553, September.
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    Cited by:

    1. Alessandra Luati & Francesca Papagni & Tommaso Proietti, 2024. "Efficient nonparametric estimation of generalised autocovariances," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 36(1), pages 23-38, January.
    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.
    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 processes; Spectral estimation; White noise tests; Feature matching; Discriminant analysis;
    All these keywords.

    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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