Abstract-Parsimonious parametric models for nonstationary random processes are useful in many applications. Here, we consider a nonstationary extension of the classical autoregressive moving-average (ARMA) model that we term the time-frequency autoregressive moving-average (TFARMA) model. This model uses frequency shifts in addition to time shifts (delays) for modeling nonstationary process dynamics. The TFARMA model and its special cases, the TFAR and TFMA models, are shown to be specific types of time-varying ARMA (AR, MA) models. They are attractive because of their parsimony for underspread processes, that is, nonstationary processes with a limited time-frequency correlation structure. We develop computationally efficient order-recursive estimators for the TFARMA, TFAR, and TFMA model parameters which are based on linear time-frequency Yule-Walker equations or on a new time-frequency cepstrum. Simulation results demonstrate that the proposed parameter estimators outperform existing estimators for time-varying ARMA (AR, MA) models with respect to accuracy and/or numerical efficiency. An application to the time-varying spectral analysis of a natural signal is also discussed.
Summary
Purpose: In recent years, a variety of methods developed in the field of linear and nonlinear time series analysis have been used to obtain reliable predictions of epileptic seizures. Because individual methods for seizure prediction so far have shown statistical significance but insufficient performance for clinical applications, we investigated possible improvements by combining algorithms capturing different aspects of electroencephalogram (EEG) dynamics.
Methods: We applied the mean phase coherence and the dynamic similarity index to long‐term continuous intracranial EEG data. The predictive performance of both methods was assessed and statistically evaluated separately, as well as by using logical “AND” and “OR” combinations.
Results: Used independently, either method resulted in a statistically significant prediction performance in only a few patients. Particularly the “AND” combination led to improved prediction performances, leading to an increase in sensitivity and/or specificity. For a maximum false prediction rate of 0.15/h, the mean sensitivity improved from about 25% for the individual methods to 43.2% for the “AND” and to 35.2% for the “OR” combination.
Discussion: This study shows that combinations of prediction methods are promising new approaches to enhance seizure prediction performance considerably. It allows merging the individual benefits of prediction methods in a complementary manner. Because either sensitivity or specificity of seizure prediction methods can be improved depending on the needs of the desired clinical application, the combination opens a new window for future use in a clinical setting.
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