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.

Generalised partial autocorrelations and the mutual information between past and future / Luati, Alessandra; Proietti, Tommaso. - STAMPA. - (2016), pp. 303-315. [10.1007/978-3-319-25826-3_14]

Generalised partial autocorrelations and the mutual information between past and future

Luati, Alessandra;
2016

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.
2016
The fascination of probability, statistics and their applications. In honour of Ole E. Barndorff-Nielsen
303
315
Generalised partial autocorrelations and the mutual information between past and future / Luati, Alessandra; Proietti, Tommaso. - STAMPA. - (2016), pp. 303-315. [10.1007/978-3-319-25826-3_14]
Luati, Alessandra; Proietti, Tommaso
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/598954
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