Generalised Partial Autocorrelations and the Mutual Information between Past and Future
University of Bologna - Department of Statistics
University of Rome II - Department of Economics and Finance
June 5, 2015
CEIS Working Paper No. 344
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.
Number of Pages in PDF File: 17
Keywords: Generalised autocovariance, Spectral models, Whittle likelihood, Reparameterisation.
JEL Classification: C22, C52
Date posted: June 6, 2015