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Generalized Linear Spectral Models for Locally Stationary Processes

In: Research Papers in Statistical Inference for Time Series and Related Models

Author

Listed:
  • Tommaso Proietti

    (Università di Roma Tor Vergata)

  • Alessandra Luati

    (Imperial College London)

  • Enzo D’Innocenzo

    (Vrije Universiteit Amsterdam)

Abstract

A class of parametric models for locally stationary processes is introduced. The class depends on a power parameter that applies to the time-varying spectrum so that it can be locally represented by a (finite low dimensional) Fourier polynomial. The coefficients of the polynomial have an interpretation as time-varying autocovariances, whose dynamics are determined by a linear combination of smooth transition functions, depending on some static parameters. Frequency domain estimation is based on the generalized Whittle likelihood and the pre-periodogram, while model selection is performed through information criteria. Change points are identified via a sequence of score tests. Consistency and asymptotic normality are proved for the parametric estimators considered in the paper, under weak assumptions on the time-varying parameters.

Suggested Citation

  • Tommaso Proietti & Alessandra Luati & Enzo D’Innocenzo, 2023. "Generalized Linear Spectral Models for Locally Stationary Processes," Springer Books, in: Yan Liu & Junichi Hirukawa & Yoshihide Kakizawa (ed.), Research Papers in Statistical Inference for Time Series and Related Models, chapter 0, pages 343-368, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-0803-5_13
    DOI: 10.1007/978-981-99-0803-5_13
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