On long memory origins and forecast horizons

Vera-Valdés, J. Eduardo

doi:10.1002/for.2651

Cited by 11 publications

(6 citation statements)

References 53 publications

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“…From figures 2-5, we find that the said autocorrelation functions demonstrate that their decay is algebraic and slower than exponential such that the area enclosed by the composite autocorrelation function curve is infinite. Such slowly decaying autocorrelation functions with non-negligible values even at long lags are typical of processes having intrinsic long-range memory and are modeled well with fractional derivatives [59,60].…”

Section: Fractional-order Systemsmentioning

confidence: 99%

Fractional-order model predictive control as a framework for electrical neurostimulation in epilepsy

et al. 2020

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Objective. Electrical neurostimulation is an increasingly adopted therapeutic methodology for neurological conditions such as epilepsy. Electrical neurostimulation devices are commonly characterized by their limited sensing, actuating, and computational capabilities. However, the sensing mechanisms are often used only for their detection potential (e.g. to detect seizures), which automatically and dynamically trigger the actuation capabilities, but ultimately deploy prespecified stimulation doses that resulted from a period of manual (and empirical) calibration. The potential information contained in the measurements acquired by the sensing mechanisms is, therefore, considerably underutilized, given that this type of stimulation strategy only entails an event-triggered relationship between the sensors and actuators of the device. Such stimulation strategies are suboptimal in general and lack theoretical guarantees regarding their performance. Approach. In order to leverage the aforementioned information, harvested during normal sensing-actuating operation, we must consider a real-time feedback (closed-loop) strategy. More precisely, the stimulation signal itself should automatically adapt based upon the state of the neurophysiological system at hand, estimated from data collected in real-time through sensors in the device. Main results. In this work, we propose a model-based approach for (real-time) closed-loop electrical neurostimulation, in which the evolution of the system is captured by a fractional-order system (FOS). More precisely, we propose a model predictive control (MPC) approach with an underlying FOS predictive model, due to the ability of fractional-order dynamics to more accurately capture the long-term dependence present in biological systems, compared to the standard linear time-invariant models. Furthermore, MPC offers, by design, an additional layer of robustness to compensate for system-model mismatch, which the more traditional strategies lack. To establish the potential of our framework, we focus on epileptic seizure mitigation by computational simulation of our proposed strategy upon seizure-like events. Lastly, we provide evidence of the effectiveness of our method on seizures simulated by commonly adopted models in the neuroscience and medical community present in the literature, as well as real seizure data as obtained from subjects with epilepsy. Significance Our study thus paves the way for the development and implementation of robust real-time closed-loop electrical neurostimulation which can then be used for the construction of more effective devices for epileptic seizure mitigation.

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Section: Fractional-order Systemsmentioning

confidence: 99%

Fractional-order model predictive control as a framework for electrical neurostimulation in epilepsy

et al. 2020

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“…where 𝛼 > 1 and 𝛽 > 0, and Γ is the Gamma function. Similar aggregated models have been analyzed for continuous-time cases (Randrianambinina & Esunge, 2022) and for discrete-time cases where there may be a correlation among elements of aggregated processes (Beran et al, 2020;Vera-Valdés, 2020). We can assume that the reversion measure 𝜋 identified by some method is ambiguous and that the true or most reasonable measure is the perturbation 𝜙(r)𝜋(dr) with some positive function 𝜙 so that 𝜙(r)𝜋(dr) becomes a new probability measure.…”

Section: Objective and Contributionmentioning

confidence: 99%

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

Yoshioka,

Yoshioka

2023

Environmetrics

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The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

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“…The properties of the fractional difference operator have been well documented in, among others, Baillie (1996) and Beran et al (2013). Moreover, fractionally integrated models obtain good forecasting performance when working with series that exhibit longrange dependence regardless of their generating process; see Bhardwaj and Swanson (2006) and Vera-Valdés (2020). Furthermore, fast algorithms have been developed to generate series using the fractional difference operator; see Jensen and Nielsen (2014).…”

Section: The Fractional Difference Operatormentioning

confidence: 99%

Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

Vera-Valdés

2021

Econometrics

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This paper used cross-sectional aggregation as the inspiration for a model with long-range dependence that arises in actual data. One of the advantages of our model is that it is less brittle than fractionally integrated processes. In particular, we showed that the antipersistent phenomenon is not present for the cross-sectionally aggregated process. We proved that this has implications for estimators of long-range dependence in the frequency domain, which will be misspecified for nonfractional long-range-dependent processes with negative degrees of persistence. As an application, we showed how we can approximate a fractionally differenced process using theoretically-motivated cross-sectional aggregated long-range-dependent processes. An example with temperature data showed that our framework provides a better fit to the data than the fractional difference operator.

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On long memory origins and forecast horizons

Cited by 11 publications

References 53 publications

Fractional-order model predictive control as a framework for electrical neurostimulation in epilepsy

Fractional-order model predictive control as a framework for electrical neurostimulation in epilepsy

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

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