Farima Modeling of Solar Flare Activity From Empirical Time Series of Soft X-Ray Solar Emission

Stanislavsky, A. A.; Burnecki, Krzysztof; Magdziarz, Marcin; Weron, Aleksander; Weron, Karina

doi:10.1088/0004-637x/693/2/1877

Cited by 45 publications

(39 citation statements)

References 51 publications

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“…ARFIMA have been already studied in the physical literature4344454647484950. However, interpretation of the various parameters in an experimental context, to the best of our knowledge, is still missing.…”

Section: Discussionmentioning

confidence: 99%

Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach

Burnecki

Kepten

Garini

et al. 2015

Sci Rep

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Accurately characterizing the anomalous diffusion of a tracer particle has become a central issue in biophysics. However, measurement errors raise difficulty in the characterization of single trajectories, which is usually performed through the time-averaged mean square displacement (TAMSD). In this paper, we study a fractionally integrated moving average (FIMA) process as an appropriate model for anomalous diffusion data with measurement errors. We compare FIMA and traditional TAMSD estimators for the anomalous diffusion exponent. The ability of the FIMA framework to characterize dynamics in a wide range of anomalous exponents and noise levels through the simulation of a toy model (fractional Brownian motion disturbed by Gaussian white noise) is discussed. Comparison to the TAMSD technique, shows that FIMA estimation is superior in many scenarios. This is expected to enable new measurement regimes for single particle tracking (SPT) experiments even in the presence of high measurement errors.

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Section: Discussionmentioning

confidence: 99%

Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors - An alternative approach

Burnecki

Kepten

Garini

et al. 2015

Sci Rep

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“…The richer classes of ARIMA and ARFIMA models that treat non-stationarity and long-memory 'red' noise as well as short-memory processes only rarely appear in astronomical studies. ARFIMA is used by Stanislavsky et al (2009) to characterized solar flaring in the X-ray band. For irregularly spaced data, the model can be reconfigured as a continuous-time process.…”

Section: Introductionmentioning

confidence: 99%

Autoregressive Planet Search: Methodology

Caceres

Feigelson

Babu

et al. 2019

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The detection of periodic signals from transiting exoplanets is often impeded by extraneous aperiodic photometric variability, either intrinsic to the star or arising from the measurement process. Frequently, these variations are autocorrelated wherein later flux values are correlated with previous ones. In this work, we present the methodology of the Autoregessive Planet Search (ARPS) project which uses Autoregressive Integrated Moving Average (ARIMA) and related statistical models that treat a wide variety of stochastic processes, as well as nonstationarity, to improve detection of new planetary transits. Providing a time series is evenly spaced or can be placed on an evenly spaced grid with missing values, these low-dimensional parametric models can prove very effective. We introduce a planet-search algorithm to detect periodic transits in the residuals after the application of ARIMA models. Our matched-filter algorithm, the Transit Comb Filter (TCF), is closely related to the traditional Box-fitting Least Squares and provides an analogous periodogram. Finally, if a previously identified or simulated sample of planets is available, selected scalar features from different stages of the analysis -the original light curves, ARIMA fits, TCF periodograms, and folded light curves -can be collectively used with a multivariate classifier to identify promising candidates while efficiently rejecting false alarms. We use Random Forests for this task, in conjunction with Receiver Operating Characteristic (ROC) curves, to define discovery criteria for new, high fidelity planetary candidates. The ARPS methodology can be applied to both evenly spaced satellite light curves and densely cadenced ground-based photometric surveys.

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“…The results we report below show clearly how long-range memory effects can change H and the propagator independently. Our results also have a bearing on the family of autoregressive and heteroscedastic processes, some of which have a bearing on anomalous diffusion [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

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confidence: 96%