Modelling Cycles in Climate Series: The Fractional Sinusoidal Waveform Process

42 Pages Posted: 25 Oct 2021

See all articles by Tommaso Proietti

Tommaso Proietti

University of Rome II - Department of Economics and Finance

Federico Maddanu

University of Rome Tor Vergata

Date Written: October 19, 2021

Abstract

The paper proposes a novel model for time series displaying persistent stationary cycles, the fractional sinusoidal waveform process. The underlying idea is to allow the parameters that regulate the amplitude and phase to evolve according to fractional noise processes. Its advantages with respect to popular alternative specifications, such as the Gegenbauer process, are twofold: the autocovariance function is available in closed form, which opens the way to exact maximum likelihood estimation; secondly the model encompasses deterministic cycles, so that discrete spectra arise as a limiting case. A generalization of the process, featuring multiple components, an additive `red noise' component and exogenous variables, provides a model for climate time series with mixed spectra. Our illustrations deal with the change in amplitude and phase of the intra-annual component of carbon dioxide concentrations in Mauna Loa, and with the estimation and the quantification of the contribution of orbital cycles to the variability of paleoclimate time series.

Keywords: Mixed Spectrum. Cyclical long memory. Paleoclimatic data.

Suggested Citation

Proietti, Tommaso and Maddanu, Federico, Modelling Cycles in Climate Series: The Fractional Sinusoidal Waveform Process (October 19, 2021). CEIS Working Paper No. 518, Available at SSRN: https://ssrn.com/abstract=3945978 or http://dx.doi.org/10.2139/ssrn.3945978

Tommaso Proietti (Contact Author)

University of Rome II - Department of Economics and Finance ( email )

Via Columbia, 2
Rome, 00133
Italy

Federico Maddanu

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

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