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.
Luati, A., and Proietti, T. (2016). Generalised partial autocorrelations and the mutual information between past and future. In M. Podolskij (a cura di), The Fascination of Probability, Statistics and their Applications. In Honour of Ole E. Barndorff-Nielsen. (pp. 303-315). Springer International Publishing [10.1007/978-3-319-25826-3_14].
Generalised partial autocorrelations and the mutual information between past and future
and Proietti, Tommaso
2016-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
