The Generalised Autocovariance Function

33 Pages Posted: 7 May 2013

See all articles by Tommaso Proietti

Tommaso Proietti

University of Rome II - Department of Economics and Finance

Alessandra Luati

University of Bologna - Department of Statistics

Date Written: April 30, 2013

Abstract

The generalised autocovariance function is defined for a stationary stochastic process as the inverse Fourier transform of the power transformation of the spectral density function. Depending on the value of the transformation parameter, this function nests the inverse and the traditional autocovariance functions. A frequency domain non-parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived. The results are employed to construct classes of tests of the white noise hypothesis, for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum.

Keywords: Stationary Gaussian processes, Non-parametric spectral estimation, White noise tests, Feature matching, Discriminant Analysis

Suggested Citation

Proietti, Tommaso and Luati, Alessandra, The Generalised Autocovariance Function (April 30, 2013). CEIS Working Paper No. 276. Available at SSRN: https://ssrn.com/abstract=2258569 or http://dx.doi.org/10.2139/ssrn.2258569

Tommaso Proietti (Contact Author)

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

Via Columbia, 2
Rome, 00133
Italy

Alessandra Luati

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
39
Abstract Views
338
PlumX Metrics