Abstract
Both parametric and non-parametric approaches to time-series analysis have advantages and drawbacks. Parametric methods, although powerful and widely used, can yield inconsistent results due to the oversimplification of the observed phenomena. They require the setting of arbitrary constants for their creation and refinement, and, although these constants relate to assumptions about the observed systems, it can lead to erroneous results when treating a very complex problem with a sizable list of unknowns. Their non-parametric counterparts, instead, are more widely applicable but present a higher detrimental sensitivity to noise and low density in the data. For the case of approximately periodic phenomena, such as human actigraphic time series, parametric methods are widely used and concepts such as acrophase are key in chronobiology, especially when studying healthy and diseased human populations. In this work, we present a non-parametric method of analysis of actigraphic time series from insomniac patients and healthy age-matched controls. The method is fully data-driven, reproduces previous results in the context of activity offset delay and, crucially, extends the concept of acrophase not only to circadian but also for ultradian spectral components.
Highlights
Both parametric and non-parametric approaches to time-series analysis have advantages and drawbacks
We present a non-parametric method of analysis of actigraphic time series from insomniac patients and healthy age-matched controls
Disruptions in circadian and ultradian rhythms between acute insomnia patients and healthy age-matched controls can be identified by the statistical properties of continuous actigraphic time series using a non-parametric model-free analysis
Summary
Both parametric and non-parametric approaches to time-series analysis have advantages and drawbacks. A key concept in the study of circadian cycles stemming from cosinor analysis [26], relates to the notion of phase in oscillatory components that make up the approximately periodic observed time series It consists of the phase of a single sinusoidal component which better fits to the empirical data, and it has been extensively used to differentiate between healthy and diseased groups. In order to avoid the difficulties discerning between noise and true signal in a multioscillatory parametric model of actigraphic recordings, non-parametric analyses work by describing the oscillatory components in terms of the Fourier or wavelet spectral decomposition directly In this manner, spectral limits are solely defined by the properties of the observations without the need for the fitting of any parameter or by the arbitrary inclusion of harmonics. The consideration of Fourier phases approximating periodic time series is a novel concept that can be extended and further studied in other cyclic phenomena such as ecosystems, sunspots, climate, traffic and other complex systems
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