Intrinsic vs. spurious long-range memory in high-frequency records of environmental radioactivity

Abstract

Donner et al components, and (iii) low-frequency variability indicating a true longrange dependent process. In the presence of such multi-scale variability, common estimators of long-range memory in time series are prone to fail if applied to the raw data without previous separation of timescales with qualitatively different dynamics.

Radon applications in geosciences – Progress & perspectives

“…[70,75]). Radon time series can also display long-range dependence, as demonstrated in this issue by Donner et al [76]. However, unveiling and quantifying these features requires the application of sophisticated nonlinear time series analysis approaches (e.g.…”

Implication of Radon Monitoring for Earthquake Surveillance Using Statistical Techniques: A Case Study of Wenchuan Earthquake

“…This chaotic regime of the time series is realized through diurnal, seasonal, multiyear, and decadal Rn cycles along with key influencing parameters [14,53,54]. Therefore, the Rn time series is subjected to fractal estimates to determine the degree of chaotic behaviour of Rn and intrinsic long-memory correlations, if any [55]. Besides this, the estimation of fractal elements for the Rn time series leads to further exploration of the underlying dynamics of physical systems such as seismic activity [56].…”

Stochastic Models for Radon Daily Time Series: Seasonality, Stationarity, and Long-Range Dependence Detection

“…Whatever the cause, these anomalies can be masked within the signal, and a way to bring them to light would be to de-noise the signal from the trend and/or periodic components (Baykut et al, 2010;Siino et al, 2019b;D'Alessandro et al, 2020). As a matter of fact, it is a challenging task to untangle and properly quantify all of these effects on the radon fluctuations because Rn time series present generally a nonstationary behavior, not constant variability over time and a long-term memory (Donner et al, 2015).…”

“…Moreover, because long-term records of environmental variables show often long-range memory, some other tools are usually applied. The fractionally integrated moving average models [ARFIMA (p,d,q)] have been widely used in the literature to describe meteorological variables (Yaya and Fashae, 2015;Bowers and Tung, 2018), pollutants and soil gas (Pan and Chen, 2008;Donner et al, 2015;Belbute and Pereira, 2017;Reisen et al, 2018), and hydrological time series (Montanari et al, 1997;Wang et al, 2007). This class of models is used when the longterm correlations in the data decay more slowly than an exponential form, that is, a typical shape of autocorrelation in the autoregressive moving average [ARMA(p,q)] processes (Box et al, 2015).…”

“…Later, the Box-Jenkins methodology often used in econometrics was applied to describe five-year-long radon time series considering a seasonal integrated, autoregressive moving averages model with exogenous variables (SARIMAX) also adding external covariates such as delayed atmospheric parameters (Stránský and Thinová, 2017). Donner et al (2015) present complementary methods that have been applied for evaluating the presence of longrange correlations and fractal scaling in environmental radon measurements.…”