Frequency domain analysis of stationary time series

Papagni, Francesca (2021) Frequency domain analysis of stationary time series, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Scienze statistiche, 33 Ciclo.
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Abstract

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Papagni, Francesca
Supervisore
Dottorato di ricerca
Ciclo
33
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
time series analysis; frequency domain analysis; asymptotic efficiency; nonparametric estimation; multivariate time series; minimum contrast estimation; covariance matrix;
URN:NBN
Data di discussione
26 Maggio 2021
URI

Altri metadati

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