To identified periodicities that are more frequent than annual and less frequent than daily we compute the power spectrum of the discrete time standardized version of our annually adjusted time series using SAS PROC SPECTRA and the Fast Fourier Transform [ 9].
Then, Fourier transformations were applied to each probe for 1-40-h periods in 15-min increments to identify periodicity and phase offset.
ARSER is a newly developed algorithm to analyze diurnal or circadian expression data by combining the time-domain and frequency-domain analyses, and was shown to be efficient in identifying periodicity in short time-series [32].
These are non-stationary and often noisy time series, causing problems in identifying periodicity.
Our methodology for identifying periodicity of short time-series worked successfully on synthetic datasets.
However, we can also identify periodicities around 320 CE, 400 CE, 630 CE, and 820 CE.
At high scales, wavelets have a small time support and are able to identify discontinuities or singularities, while at low scales wavelets have a larger time support and can identify periodicities.
While the previously mentioned methods are mostly used to identify periodicities or help synchronize time series data, other approaches exist to explore more general properties of a system, like stability and attractor dynamics, feedback loops, deterministic and stochastic behavior [ 49].
To identify periodic patterns that may appear in nuclesomal sequences wrapping different histone variants, we employed autocorrelation analysis, which was sucessfully applied to detect hidden sequence periodicities in sets of DNA sequences [ 47, 48](see Methods).
We identified latent periodicity in catalytic domains of approximately 85% of annotated serine threonine and tyrosine protein kinases.
