Generalised Linear Spectral Models

27 Pages Posted: 7 Oct 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: October 3, 2013

Abstract

In this chapter we consider a class of parametric spectrum estimators based on a generalized linear model for exponential random variables with power link. The power transformation of the spectrum of a stationary process can be expanded in a Fourier series, with the coefficients representing generalised autocovariances. Direct Whittle estimation of the coefficients is generally unfeasible, as they are subject to constraints (the autocovariances need to be a positive semidefinite sequence). The problem can be overcome by using an ARMA representation for the power transformation of the spectrum. Estimation is carried out by maximising the Whittle likelihood, whereas the selection of a spectral model, as a function of the power transformation parameter and the ARMA orders, can be carried out by information criteria. The proposed methods are applied to the estimation of the inverse autocorrelation function and the related problem of selecting the optimal interpolator, and for the identification of spectral peaks. More generally, they can be applied to spectral estimation with possibly misspecified models.

Keywords: generalized linear models, iteratively weighted least squares, frequency domain methods

JEL Classification: C22, C52

Suggested Citation

Proietti, Tommaso and Luati, Alessandra, Generalised Linear Spectral Models (October 3, 2013). CEIS Working Paper No. 290. Available at SSRN: https://ssrn.com/abstract=2335356 or http://dx.doi.org/10.2139/ssrn.2335356

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

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