Generalised partial autocorrelations and the mutual information between past and future

Tommaso Proietti and Alessandra Luati ()
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Alessandra Luati: University of Bologna, Postal: Dipartimento di Scienze Statistiche «Paolo Fortunati» Via Belle Arti, 41 Bologna, Italy

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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 generalized 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.

Keywords: Generalised autocovariance; Spectral models; Whittle likelihood; Reparameterisation (search for similar items in EconPapers)
JEL-codes: C22 C52 (search for similar items in EconPapers)
Pages: 14
Date: 2015-05-25
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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https://repec.econ.au.dk/repec/creates/rp/15/rp15_24.pdf (application/pdf)

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Working Paper: Generalised partial autocorrelations and the mutual information between past and future (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:aah:create:2015-24

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