The Generalised Autocovariance Function
Associate Professor Tommaso Proietti, Discipline of Business Analytics, University of Sydney Business School
23rd Nov 2012 11:00 am - Room 498 Merewether Building H04
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.