Generalised Partial Autocorrelations and the Mutual Information between Past and Future

17 Pages Posted: 6 Jun 2015  

Alessandra Luati

University of Bologna - Department of Statistics

Tommaso Proietti

University of Rome II - Department of Economics and Finance

Date Written: June 5, 2015

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.

Keywords: Generalised autocovariance, Spectral models, Whittle likelihood, Reparameterisation.

JEL Classification: C22, C52

Suggested Citation

Luati, Alessandra and Proietti, Tommaso, Generalised Partial Autocorrelations and the Mutual Information between Past and Future (June 5, 2015). CEIS Working Paper No. 344. Available at SSRN: https://ssrn.com/abstract=2615064 or http://dx.doi.org/10.2139/ssrn.2615064

Alessandra Luati

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

Tommaso Proietti (Contact Author)

University of Rome II - Department of Economics and Finance ( email )

Via Columbia n.2
Rome, rome 00100
Italy

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