Generalised Partial Autocorrelations and the Mutual Information Between Past and Future

Alessandra Luati () and Tommaso Proietti
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Alessandra Luati: University of Bologna, Department of Statistics

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 303-315 from Springer

Abstract: 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 [1] 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 autocovariances; Spectral autoregressive models; Information regularity coefficient (search for similar items in EconPapers)
Date: 2016
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Working Paper: Generalised partial autocorrelations and the mutual information between past and future (2015)
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:spr:sprchp:978-3-319-25826-3_14

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DOI: 10.1007/978-3-319-25826-3_14

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