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Inverse Autocovariances And A Measure Of Linear Determinism For A Stationary Process

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  • Francesco Battaglia

Abstract

. The inverse autocorrelations and autocovariances of a stationary stochastic process are generally used in the identification of ARMA models and linear systems, but they are also useful for studying linear relations inside the process as a whole. Using inverse autocovariances, for any stationary process an ‘inverse process’ may be defined which may be considered a minimum variance linear filter, and turns out to be the best linear two‐sided interpolator for one unknown value. Basing on these results an index of linear determinism is introduced to measure to what degree a stationary process satisfies a linear deterministic constraint. The behaviour of the index for ARMA processes is finally examined.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:4:y:1983:i:2:p:79-87
    DOI: 10.1111/j.1467-9892.1983.tb00360.x
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    Cited by:

    1. Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CREATES Research Papers 2013-34, Department of Economics and Business Economics, Aarhus University.
    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. Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    4. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June.
    5. Tommaso Proietti & Alessandra Luati, 2015. "Generalised partial autocorrelations and the mutual information between past and future," CREATES Research Papers 2015-24, Department of Economics and Business Economics, Aarhus University.
    6. Roberto Baragona & Francesco Battaglia, 1995. "Linear Interpolators And The Inverse Correlation Function Of Non‐Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 531-538, November.
    7. Angela Ferretti & L. Ippoliti & P. Valentini & R. J. Bhansali, 2023. "Long memory conditional random fields on regular lattices," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    8. Maravall, Agustín & Peña, Daniel, 1992. "Missing observations and additive outliers in time series models," UC3M Working papers. Economics 2888, Universidad Carlos III de Madrid. Departamento de Economía.

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