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Generalised partial autocorrelations and the mutual information between past and future

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Abstract

The paper introduces the generalised partial autocorrelation (GPAC) coefficients of a stationary stochastic process. The latter are related to the generalised autocovariances, the inverse Fourier transform coefficients of a power transformation of the spectral density function. By interpreting the generalised partial autocorrelations as the partial autocorrelation coefficients of an auxiliary process, we derive their properties and relate them to essential features of the original process. Based on a parameterisation suggested by Barndorff-Nielsen and Schou (1973) and on Whittle likelihood, we develop an estimation strategy for the GPAC coefficients. We further prove that the GPAC coefficients can be used to estimate the mutual information between the past and the future of a time series.

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  • Alessandra Luati & Tommaso Proietti, 2015. "Generalised partial autocorrelations and the mutual information between past and future," CEIS Research Paper 344, Tor Vergata University, CEIS, revised 05 Jun 2015.
    • Handle: RePEc:rtv:ceisrp:344
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    1. 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.
    2. Lei Li & Zhongjie Xie, 1996. "Model Selection And Order Determination For Time Series By Information Between The Past And The Future," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(1), pages 65-84, January.
    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. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
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    More about this item

    Keywords

    Generalised autocovariance; Spectral models; Whittle likelihood; Reparameterisation.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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