Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare

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Variability is defined as the propensity at which a given signal is likely to change. There are many choices for measuring variability, and it is not generally known which ones offer better properties. This paper compares different variability metrics applied to irregularly (nonuniformly) sampled time series, which have important clinical applications, particularly in mental healthcare. Using both synthetic and real patient data, we identify the most robust and interpretable variability measures out of a set 21 candidates. Some of these candidates are also proposed in this work based on the absolute slopes of the time series. An additional synthetic data experiment shows that when the complete time series is unknown, as it happens with real data, a non-negligible bias that favors normalized and/or metrics based on the raw observations of the series appears. Therefore, only the results of the synthetic experiments, which have access to the full series, should be used to draw conclusions. Accordingly, the median absolute deviation of the absolute value of the successive slopes of the data is the best way of measuring variability for this kind of time series.
Ecological momentary assessment (EMA), Hawkes process, Irregularly sampled time series, Variability
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Bonilla-Escribano, P., Ramírez, D., Porras-Segovia, A., & Artés-Rodríguez, A. (2021). Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare. Mathematics, 9(1), 71.