  The Kolomogorov-Zurbenko periodogram with DiRienzo-Zurbenko algorithm
smoothing is the state-of-the-art method for spectral analysis of time series
data. Because this approach assumes that a sinusoidal model underlies
time-series data and because its algorithms are adaptive in nature, it is
superior to traditional use of autoregressive integral moving average (ARIMA)
algorithms. This article begins with a presentation of its statistical
derivation and development followed by instructions for accessing and utilizing
this approach within the R statistical program platform. The discussion then
turns to a presentation of its theoretical and practical limits with regard to
sensitivity (i.e., ability to detect weak signals), accuracy (i.e., ability to
correctly identify signal frequencies), resolution (i.e., ability to resolve
signals with close frequencies), and robustness with respect to missing data
(i.e., sensitivity and accuracy despite high levels of missingness). Next using
a simulated time series in which two signals close in frequency are embedded in
significant amounts of random noise, the predictive power of this approach is
compared to the traditional ARIMA approach, with support also garnered for its
being robust even in the face of significant levels of missing data. The
article concludes with brief descriptions of studies across a range of
scientific disciplines that have capitalized on the power of the
Kolmogorov-Zurbenko periodogram with DiRienzo-Zurbenko algorithm smoothing.
