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\begin{document}

\title{Power Spectral Density Background Estimate and Signal Detection via the
Multitaper Method.}



\author[1,1]{Simone Di Matteo}%
\author[2,2]{Nicholeen Mary Viall}%
\author[3,3]{Larry Kepko}%
\affil[1]{Catholic University of America at NASA-GSFC}%
\affil[2]{NASA GSFC}%
\affil[3]{NASA Goddard Space Flight Center}%


\vspace{-1em}



  
  \date{June 11, 2024}


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\begin{abstract}
We present a new spectral analysis method for the identification of
periodic signals in geophysical time series. We evaluate the power
spectral density with the adaptive multitaper method, a non-parametric
spectral analysis technique suitable for time series characterized by
colored power spectral density. Our method provides a maximum likelihood
estimation of the power spectral density background according to four
different models. It includes the option for the models to be fitted on
four smoothed versions of the power spectral density when there is a
need to reduce the influence of power enhancements due to periodic
signals. We use a statistical criterion to select the best background
representation among the different smoothing+model pairs. Then, we
define the confidence thresholds to identify the power spectral density
enhancements related to the occurrence of periodic fluctuations (\selectlanguage{greek}γ
\selectlanguage{english}test). We combine the results with those obtained with the multitaper
harmonic F test, an additional complex-valued regression analysis from
which it is possible to estimate the amplitude and phase of the signals.
We demonstrate the algorithm on Monte Carlo simulations of synthetic
time series and a case study of magnetospheric field fluctuations
directly driven by periodic density structures in the solar wind. The
method is robust and flexible. Our procedure is freely available as a
stand-alone IDL code at https://zenodo.org/record/3703168. The modular
structure of our methodology allows the introduction of new smoothing
methods and models to cover additional types of time series. The
flexibility and extensibility of the technique makes it broadly suitable
to any discipline.%
\end{abstract}%



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