Stochastic delay differential equations and related autoregressive models

Basse-O'Connor, Andreas; Nielsen, Mikkel Slot; Pedersen, John; Rohde, Victor

doi:10.1080/17442508.2019.1635601

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Based on this, we chose a so‐called stochastic delay differential equation (SDDE) as modeling framework. Note that the SDDE is a generalized version of the continuous‐time linear autoregressive model (Basse‐O'Connor et al ., 2020). The SDDE is a multivariate (possibly non‐stationary and nonlinear) SDE explaining co‐variation between variables of a dynamical system, as well as co‐variation between time‐lagged versions of these variables.…”

Section: Methodsmentioning

confidence: 99%

Estimating stratospheric polar vortex strength using ambient ocean‐generated infrasound and stochastics‐based machine learning

Vorobeva,

Eggen,

Midtfjord

et al. 2024

Quart J Royal Meteoro Soc

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There are sparse opportunities for direct measurement of upper stratospheric winds, yet improving their representation in subseasonal‐to‐seasonal prediction models can have significant benefits. There is solid evidence from previous research that global atmospheric infrasound waves are sensitive to stratospheric dynamics. However, there is a lack of results providing a direct mapping between infrasound recordings and polar‐cap upper stratospheric winds. The global International Monitoring System (IMS), which monitors compliance with the Comprehensive Nuclear‐Test‐Ban Treaty, includes ground‐based stations that can be used to characterize the infrasound soundscape continuously. In this study, multi‐station IMS infrasound data were utilized along with a machine‐learning supported stochastic model, Delay‐SDE‐net, to demonstrate how a near‐real‐time estimate of the polar‐cap averaged zonal wind at 1‐hPa pressure level can be found from infrasound data. The infrasound was filtered to a temporal low‐frequency regime dominated by microbaroms, which are ambient‐noise infrasonic waves continuously radiated into the atmosphere from nonlinear interaction between counter‐propagating ocean surface waves. Delay‐SDE‐net was trained on 5 years (2014–2018) of infrasound data from three stations and the ERA5 reanalysis 1‐hPa polar‐cap averaged zonal wind. Using infrasound in 2019–2020 for validation, we demonstrate a prediction of the polar‐cap averaged zonal wind, with an error standard deviation of around 12 m·s compared with ERA5. These findings highlight the potential of using infrasound data for near‐real‐time measurements of upper stratospheric dynamics. A long‐term goal is to improve high‐top atmospheric model accuracy, which can have significant implications for weather and climate prediction.

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Section: Methodsmentioning

confidence: 99%

Estimating stratospheric polar vortex strength using ambient ocean‐generated infrasound and stochastics‐based machine learning

Vorobeva,

Eggen,

Midtfjord

et al. 2024

Quart J Royal Meteoro Soc

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“…ARMA models are discussed in detail by Box and Jenkins [4]. The basic concept of using artificial acceleration in the seismic analysis was proposed by Housner and Jennings [5] and Jack [6], and other researchers have studied the correlation between model parameters [7,8].…”

Section: Introductionmentioning

confidence: 99%

A Nonstationary Mathematical Model for Acceleration Time Series

Brahimi¹,

Smain²

2021

MMEP

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The choice of nonstationary stochastic models for the study is fully justified by the limitation of acceleration time series number. The three acceleration time series under consideration are used to generate a new, artificial series of ten per historical one using autoregressive moving average model. Subsequently, the average of nonlinear is utilized for the ten acceleration time series in order to obtain the spectral response of a system with single degree of freedom. Modeling of acceleration time series involves critical estimation of metrics that characterize nonstationary acceleration time series. Thus, for the stiffness degrading systems and bilinear systems, the metrics of hysteretic energy demand and displacement ductility demand during displacement are used. The applicability of artificially generated acceleration time series for the qualitative description of information was shown. More specifically, ARMA (2,2) showed the best results in the study for three accelerated time series through nonlinear response analysis. In addition, as a result, normalized hysteretic energy demand, empirically valid displacement ductility relationships, and model parameters were proposed.

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“…e existing forecasting models are mainly divided into three categories: time series models, neural network models, and hybrid models. Time series models mainly include exponential smoothing [9], differential autoregressive moving average model [10], spectral analysis model [11], and Kalman filter [12]. When the historical data and the predicted data differ greatly, the performance of the above model is severely degraded, and it is not suitable for such a sudden scene.…”

Section: Introductionmentioning

confidence: 99%

Combination Forecast of Economic Chaos Based on Improved Genetic Algorithm

Yang

2021

Complexity

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The deterministic economic system will also produce chaotic dynamic behaviour, so economic chaos is getting more and more attention, and the research of economic chaos forecasting methods has become an important topic at present. The traditional economic chaos forecasting models are mostly based on large samples, but in actual production activities, there are a large number of small-sample economic chaos problems, and there is still no effective solution. This paper proposes a combined forecasting model based on the traditional economic chaos forecasting method. First of all, through the decision tree classification, priority selection of features, rough prediction is achieved. Secondly, we use BP neural network to make secondary prediction. Because the initial weight is randomly selected, it is easy to fall into the defect of local minimum. This paper optimizes the BP neural network. Finally, the decision tree model and the BP neural network model optimized by the improved genetic algorithm are combined, and the combined model is optimized by the improved GA. This method can take advantage of many prediction models and combine the prediction information of multiple different prediction models to effectively improve the fitting ability of the model and improve the prediction accuracy.

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Stochastic delay differential equations and related autoregressive models

Cited by 5 publications

References 21 publications

Estimating stratospheric polar vortex strength using ambient ocean‐generated infrasound and stochastics‐based machine learning

Estimating stratospheric polar vortex strength using ambient ocean‐generated infrasound and stochastics‐based machine learning

A Nonstationary Mathematical Model for Acceleration Time Series

Combination Forecast of Economic Chaos Based on Improved Genetic Algorithm

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