Generation of Causal Time Series arising from Spectra of Narrow-Band Asymmetric Peaks.

Astronomy and Astrophysics – Astronomy

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7522 Helioseismology

Scientific paper

Synthetic time series with known spectral properties are frequently used in the development of analysis techniques, most commonly by assigning random phases to an amplitude spectrum with the desired properties - an approach with significant limitations. For narrow band peaks of the sort encountered in helioseismology, a simple auto-regressive [AR] description yields a physically realisable signal quite naturally. In fact, a second-order AR model is just a discrete representation of the second-order differential equation giving rise to the modes. It is now widely appreciated that the profiles of helioseismic resonances are significantly asymmetric, and this can be incorporated into the generation of artificial time series quite simply by extending the AR approach to include moving averages [MA] excitation. This ARMA model provides an immediate source of the correlated noise that has been invoked to describe the asymmetries. The NSO is sponsored by the National Science Foundation through a cooperative agreement with the Association of Universities for Research in Astronomy, Inc.

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