scholarly journals Robust Methods for Soft Clustering of Multidimensional Time Series

2021 ◽  
Vol 7 (1) ◽  
pp. 60
Author(s):  
Ángel López-Oriona ◽  
Pierpaolo D’Urso ◽  
José A. Vilar ◽  
Borja Lafuente-Rego
Keyword(s):  
Time Series ◽  
Spectral Density ◽  
Simulation Study ◽  
Robust Methods ◽  
Robust Algorithms ◽  
Fuzzy C Means ◽  
Multidimensional Time Series ◽  
Cross Spectral Density ◽  
Alternative Procedures ◽  
Underlying Processes

Three robust algorithms for clustering multidimensional time series from the perspective of underlying processes are proposed. The methods are robust extensions of a fuzzy C-means model based on estimates of the quantile cross-spectral density. Robustness to the presence of anomalous elements is achieved by using the so-called metric, noise and trimmed approaches. Analyses from a wide simulation study indicate that the algorithms are substantially effective in coping with the presence of outlying series, clearly outperforming alternative procedures. The usefulness of the suggested methods is also highlighted by means of a specific application.

scholarly journals The CSS and The Two-Staged Methods for Parameter Estimation in SARFIMA Models

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Erol Egrioglu ◽  
Cagdas Hakan Aladag ◽  
Cem Kadilar
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Long Memory ◽  
Moving Average ◽  
Mean Square ◽  
Sample Sizes ◽  
Advantages And Disadvantages

Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models are used in the analysis of seasonal long memory-dependent time series. Two methods, which are conditional sum of squares (CSS) and two-staged methods introduced by Hosking (1984), are proposed to estimate the parameters of SARFIMA models. However, no simulation study has been conducted in the literature. Therefore, it is not known how these methods behave under different parameter settings and sample sizes in SARFIMA models. The aim of this study is to show the behavior of these methods by a simulation study. According to results of the simulation, advantages and disadvantages of both methods under different parameter settings and sample sizes are discussed by comparing the root mean square error (RMSE) obtained by the CSS and two-staged methods. As a result of the comparison, it is seen that CSS method produces better results than those obtained from the two-staged method.

A New Random Data Description and Its Use in Transferring Road Roughness to Vehicle Response

1974 ◽  
Vol 96 (2) ◽  
pp. 676-679 ◽  
Author(s):  
J. C. Wambold ◽  
W. H. Park ◽  
R. G. Vashlishan
Keyword(s):  
Spectral Density ◽  
Frequency Distribution ◽  
Descriptive Analysis ◽  
Joint Probability ◽  
Amplitude Distribution ◽  
Matrix Functions ◽  
Initial Portion ◽  
Power Spectral ◽  
Road Roughness ◽  
Cross Spectral Density

The initial portion of the paper discusses the more conventional method of obtaining a vehicle transfer function where phase and magnitude are determined by dividing the cross spectral density of the input/output by the power spectral density (PSD) of the input. The authors needed a more descriptive analysis (over PSD) and developed a new signal description called Amplitude Frequency Distribution (AFD); a discrete joint probability of amplitude and frequency with the advantage of retaining amplitude distribution as well as frequency distribution. A better understanding was obtained, and transfer matrix functions were developed using AFD.

scholarly journals Using logic regression to characterize extreme heat exposures and their health associations: a time-series study of emergency department visits in Atlanta

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Shan Jiang ◽  
Joshua L. Warren ◽  
Noah Scovronick ◽  
Shannon E. Moss ◽  
Lyndsey A. Darrow ◽  
...  
Keyword(s):  
Emergency Department ◽  
Time Series ◽  
Health Outcomes ◽  
Simulation Study ◽  
Heat Exposure ◽  
Emergency Department Visits ◽  
Extreme Heat ◽  
Logic Regression ◽  
Adverse Health ◽  
Adverse Health Outcomes

Abstract Background Short-term associations between extreme heat events and adverse health outcomes are well-established in epidemiologic studies. However, the use of different exposure definitions across studies has limited our understanding of extreme heat characteristics that are most important for specific health outcomes or subpopulations. Methods Logic regression is a statistical learning method for constructing decision trees based on Boolean combinations of binary predictors. We describe how logic regression can be utilized as a data-driven approach to identify extreme heat exposure definitions using health outcome data. We evaluated the performance of the proposed algorithm in a simulation study, as well as in a 20-year time-series analysis of extreme heat and emergency department visits for 12 outcomes in the Atlanta metropolitan area. Results For the Atlanta case study, our novel application of logic regression identified extreme heat exposure definitions that were associated with several heat-sensitive disease outcomes (e.g., fluid and electrolyte imbalance, renal diseases, ischemic stroke, and hypertension). Exposures were often characterized by extreme apparent minimum temperature or maximum temperature over multiple days. The simulation study also demonstrated that logic regression can successfully identify exposures of different lags and duration structures when statistical power is sufficient. Conclusion Logic regression is a useful tool for identifying important characteristics of extreme heat exposures for adverse health outcomes, which may help improve future heat warning systems and response plans.

scholarly journals Time series analysis of trial-to-trial variability of MEG power spectrum during rest state, unattented listening and frequency-modulated tones classification

2021 ◽  
Author(s):  
Lech Kipiński ◽  
Wojciech Kordecki
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Power Spectrum ◽  
Spectral Density ◽  
Cognitive Task ◽  
Clinical Neuroscience ◽  
Rest State ◽  
Short Time ◽  
Low Complex ◽  
Dominant Frequencies

AbstractThe nonstationarity of EEG/MEG signals is important for understanding the functioning of human brain. From the previous research we know that even very short, i.e. 250—500ms MEG signals are variance-nonstationary. The covariance of stochastic process is mathematically associated with its spectral density, therefore we investigate how the spectrum of such nonstationary signals varies in time.We analyze the data from 148-channel MEG, that represent rest state, unattented listening and frequency-modulated tones classification. We transform short-time MEG signals to the frequency domain using the FFT algorithm and for the dominant frequencies 8—12 Hz we prepare the time series representing their trial-to-trial variability. Then, we test them for level- and trend-stationarity, unit root, heteroscedasticity and gaussianity and based on their properties we propose the ARMA-modelling for their description.The analyzed time series have the weakly stationary properties independently of the functional state of brain and localization. Only their small percentage, mostly related to the cognitive task, still presents nonstationarity. The obtained mathematical models show that the spectral density of analyzed signals depends on only 2—3 previous trials.The presented method has limitations related to FFT resolution and univariate models, but it is not computationally complicated and allows to obtain a low-complex stochastic models of the EEG/MEG spectrum variability.Although the physiological short-time MEG signals are in principle nonstationary in time domain, its power spectrum at the dominant frequencies varies as weakly stationary stochastic process. Described technique has the possible applications in prediction of the EEG/MEG spectral properties in theoretical and clinical neuroscience.

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