2,477 research outputs found
Time series forecasting with the WARIMAX-GARCH method
It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (WARIMAX-GARCH) method, is proposed to improve predictive performance and accuracy but also to address, at least in part, the problem of unavailable EVs. Basically, the WARIMAX-GARCH method obtains Wavelet âEVsâ (WEVs) from Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (ARIMAX-GARCH) models applied to Wavelet Components (WCs) that are initially determined from the underlying time series. The WEVs are, in fact, treated by the WARIMAX-GARCH method as if they were conventional EVs. Similarly to GARCH and ARIMA-GARCH models, the WARIMAX-GARCH method is suitable for time series exhibiting non-linear characteristics such as conditional variance that depends on past values of observed data. However, unlike those, it can explicitly model frequency domain patterns in the series to help improve predictive performance. An application to a daily time series of dam displacement in Brazil shows the WARIMAX-GARCH method to remarkably outperform the ARIMA-GARCH method, as well as the (multi-layer perceptron) Artificial Neural Network (ANN) and its wavelet version referred to as Wavelet Artificial Neural Network (WANN) as in [1], on statistical measures for both in-sample and out-of-sample forecasting
Efficient transfer entropy analysis of non-stationary neural time series
Information theory allows us to investigate information processing in neural
systems in terms of information transfer, storage and modification. Especially
the measure of information transfer, transfer entropy, has seen a dramatic
surge of interest in neuroscience. Estimating transfer entropy from two
processes requires the observation of multiple realizations of these processes
to estimate associated probability density functions. To obtain these
observations, available estimators assume stationarity of processes to allow
pooling of observations over time. This assumption however, is a major obstacle
to the application of these estimators in neuroscience as observed processes
are often non-stationary. As a solution, Gomez-Herrero and colleagues
theoretically showed that the stationarity assumption may be avoided by
estimating transfer entropy from an ensemble of realizations. Such an ensemble
is often readily available in neuroscience experiments in the form of
experimental trials. Thus, in this work we combine the ensemble method with a
recently proposed transfer entropy estimator to make transfer entropy
estimation applicable to non-stationary time series. We present an efficient
implementation of the approach that deals with the increased computational
demand of the ensemble method's practical application. In particular, we use a
massively parallel implementation for a graphics processing unit to handle the
computationally most heavy aspects of the ensemble method. We test the
performance and robustness of our implementation on data from simulated
stochastic processes and demonstrate the method's applicability to
magnetoencephalographic data. While we mainly evaluate the proposed method for
neuroscientific data, we expect it to be applicable in a variety of fields that
are concerned with the analysis of information transfer in complex biological,
social, and artificial systems.Comment: 27 pages, 7 figures, submitted to PLOS ON
Inferring collective dynamical states from widely unobserved systems
When assessing spatially-extended complex systems, one can rarely sample the
states of all components. We show that this spatial subsampling typically leads
to severe underestimation of the risk of instability in systems with
propagating events. We derive a subsampling-invariant estimator, and
demonstrate that it correctly infers the infectiousness of various diseases
under subsampling, making it particularly useful in countries with unreliable
case reports. In neuroscience, recordings are strongly limited by subsampling.
Here, the subsampling-invariant estimator allows to revisit two prominent
hypotheses about the brain's collective spiking dynamics:
asynchronous-irregular or critical. We identify consistently for rat, cat and
monkey a state that combines features of both and allows input to reverberate
in the network for hundreds of milliseconds. Overall, owing to its ready
applicability, the novel estimator paves the way to novel insight for the study
of spatially-extended dynamical systems.Comment: 7 pages + 12 pages supplementary information + 7 supplementary
figures. Title changed to match journal referenc
Effect of visual feedback on the occipital-parietal-motor network in Parkinson's disease with freezing of gait.
Freezing of gait (FOG) is an elusive phenomenon that debilitates a large number of Parkinson's disease (PD) patients regardless of stage of disease, medication status, or deep brain stimulation implantation. Sensory feedback cues, especially visual feedback cues, have been shown to alleviate FOG episodes or even prevent episodes from occurring. Here, we examine cortical information flow between occipital, parietal, and motor areas during the pre-movement stage of gait in a PD-with-FOG patient that had a strong positive behavioral response to visual cues, one PD-with-FOG patient without any behavioral response to visual cues, and age-matched healthy controls, before and after training with visual feedback. Results for this case study show differences in cortical information flow between the responding PD-with-FOG patient and the other two subject types, notably, an increased information flow in the beta range. Tentatively suggesting the formation of an alternative cortical sensory-motor pathway during training with visual feedback, these results are proposed as subject for further verification employing larger cohorts of patients
Epicasting: An Ensemble Wavelet Neural Network (EWNet) for Forecasting Epidemics
Infectious diseases remain among the top contributors to human illness and
death worldwide, among which many diseases produce epidemic waves of infection.
The unavailability of specific drugs and ready-to-use vaccines to prevent most
of these epidemics makes the situation worse. These force public health
officials and policymakers to rely on early warning systems generated by
reliable and accurate forecasts of epidemics. Accurate forecasts of epidemics
can assist stakeholders in tailoring countermeasures, such as vaccination
campaigns, staff scheduling, and resource allocation, to the situation at hand,
which could translate to reductions in the impact of a disease. Unfortunately,
most of these past epidemics exhibit nonlinear and non-stationary
characteristics due to their spreading fluctuations based on seasonal-dependent
variability and the nature of these epidemics. We analyse a wide variety of
epidemic time series datasets using a maximal overlap discrete wavelet
transform (MODWT) based autoregressive neural network and call it EWNet model.
MODWT techniques effectively characterize non-stationary behavior and seasonal
dependencies in the epidemic time series and improve the nonlinear forecasting
scheme of the autoregressive neural network in the proposed ensemble wavelet
network framework. From a nonlinear time series viewpoint, we explore the
asymptotic stationarity of the proposed EWNet model to show the asymptotic
behavior of the associated Markov Chain. We also theoretically investigate the
effect of learning stability and the choice of hidden neurons in the proposal.
From a practical perspective, we compare our proposed EWNet framework with
several statistical, machine learning, and deep learning models. Experimental
results show that the proposed EWNet is highly competitive compared to the
state-of-the-art epidemic forecasting methods
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