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Register a new userOn unified framework for continuous-time grey models: an integral matching perspective
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Added by
Baolei Wei
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Since most of the research about grey forecasting models is focused on developing novel models and improving accuracy, relatively limited attention has been paid to the modelling mechanism and relationships among diverse kinds of models. This paper aims to unify and reconstruct continuous-time grey models, highlighting the differences and similarities among different models. First, the unified form of grey models is proposed and simplified into a reduced-order ordinary differential equation. Then, the integral matching that consists of integral transformation and least squares, is proposed to estimate the structural parameter and initial value simultaneously. The cumulative sum operator, an essential element in grey modelling, proves to be the discrete approximation of the integral transformation formula. Next, grey models are reconstructed by the integral matching-based ordinary differential equations. Finally, the existing grey models are compared with the reconstructed models through extensive simulation studies, and a real-world example shows how to apply and further verify the reconstructed model.
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Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited attention has been paid to the relationship among diverse models and the modelling mechanism. The current paper proposes a unified framework and reconstructs the unified model from an integro-differential equation perspective. First, we propose a methodological framework that subsumes various nonlinear grey system models as special cases, providing a cumulative sum series-orientated modelling paradigm. Then, by introducing an integral operator, the unified model is reduced to an equivalent integro-differential equation; on this basis, the structural parameters and initial value are estimated simultaneously via the integral matching approach. The modelling procedure comparison further indicates that the integral matching-based integro-differential equation provides a direct modelling paradigm. Next, large-scale Monte Carlo simulations are conducted to compare the finite sample performance, and the results show that the reduced model has higher accuracy and robustness to noise. Applications of forecasting the municipal sewage discharge and water consumption in the Yangtze River Delta of China further illustrate the effectiveness of the reconstructed nonlinear grey models.
As an essential characteristics of fractional calculus, the memory effect is served as one of key factors to deal with diverse practical issues, thus has been received extensive attention since it was born. By combining the fractional derivative with memory effects and grey modeling theory, this paper aims to construct an unified framework for the commonly-used fractional grey models already in place. In particular, by taking different kernel and normalization functions, this framework can deduce some other new fractional grey models. To further improve the prediction performance, the four popular intelligent algorithms are employed to determine the emerging coefficients for the UFGM(1,1) model. Two published cases are then utilized to verify the validity of the UFGM(1,1) model and explore the effects of fractional accumulation order and initial value on the prediction accuracy, respectively. Finally, this model is also applied to dealing with two real examples so as to further explain its efficacy and equally show how to use the unified framework in practical applications.
We use grey forecast model to predict the future energy consumption of four states in the U.S, and make some improvments to the model.
Continuous-time assessments of game outcomes in sports have become increasingly common in the last decade. In American football, only discrete-time estimates of play value were possible, since the most advanced public football datasets were recorded at the play-by-play level. While measures such as expected points and win probability are useful for evaluating football plays and game situations, there has been no research into how these values change throughout the course of a play. In this work, we make two main contributions: First, we introduce a general framework for continuous-time within-play valuation in the National Football League using player-tracking data. Our modular framework incorporates several modular sub-models, to easily incorporate recent work involving player tracking data in football. Second, we use a long short-term memory recurrent neural network to construct a ball-carrier model to estimate how many yards the ball-carrier is expected to gain from their current position, conditional on the locations and trajectories of the ball-carrier, their teammates and opponents. Additionally, we demonstrate an extension with conditional density estimation so that the expectation of any measure of play value can be calculated in continuous-time, which was never before possible at such a granular level.
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