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Generalised Linear Spectral Models

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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.

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  • Tommaso Proietti & Alessandra Luati, 2013. "Generalised Linear Spectral Models," CEIS Research Paper 290, Tor Vergata University, CEIS, revised 03 Oct 2013.
    • Handle: RePEc:rtv:ceisrp:290
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    1. Murray A. Cameron & T. Rolf Turner, 1987. "Fitting Models to Spectra Using Regression Packages," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(1), pages 47-57, March.
    2. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
    3. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
    4. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
    5. Alessandra Luati & Tommaso Proietti, 2010. "Hyper‐spherical and elliptical stochastic cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(3), pages 169-181, May.
    6. Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    7. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    8. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
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    1. Tommaso Proietti, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," CEIS Research Paper 319, Tor Vergata University, CEIS, revised 30 Jul 2014.

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    More about this item

    Keywords

    generalized linear models; iteratively weighted least squares; frequency domain methods;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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