After obtaining the light curves for both NuSTAR and Swift/BAT, we will then proceed to analyze them by constructing the PSD for each AGN and each instrument. However there is first the issue of gaps in the light curves. Gaps occur for a variety of reasons. For Swift/BAT, passes over the South Atlantic Anomaly, slewing, and down time cause the detectors to be turned off and produce gaps. For NuSTAR, the main source of gaps is occultation by the Earth. The different causes of the gaps therefore produce different patterns in the light curves. Gaps in Swift/BAT light curves are more randomly distributed while NuSTAR’s are highly periodic.
Gaps in light curves and how to deal with them have always been a key problem in time series analysis. Different methods have been employed including linear interpolation and drawing from a Gaussian distribution with mean and standard deviation derived from the light curve itself. All of these methods however will have some sort of effect on the measured PSD and involve “simulating” information where none exists.
\citet{Zoghbi_2013}, however, formulated a novel algorithm for constructing the PSD without having to fill in the gaps. The \citet{Zoghbi_2013} method calculates the maximum likelihood estimate of the PSD in user-defined frequency bins, taking advantage of the relationship between the PSD and the autocorrelation function. In this way, there is no need to fill in the gaps with an ad-hoc technique. \citet{Zoghbi_2013} demonstrates the missing information is reflected in the larger error bars in the frequency bins containing the gap periodicity. \citet{Zoghbi_2013} also thoroughly demonstrated through simulations that their new maximum likelihood can accurately reconstruct typical AGN PSDs from light curves with periodic gaps similar to those inherent for NuSTAR (Figure \ref{fig:zoghbi_psd}).