Diffusions for global optimizations
SIAM Journal on Control and Optimization
Stochastic approximation and optimization of random systems
Stochastic approximation and optimization of random systems
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
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We present a new approach to the problem of time series modelling that captures the invariant distribution of time series data within the model. This is particularly relevant in modelling economic and financial time series, such as oil prices, that exhibit clustering around a few preferred market modes. We propose a potential function approach which determines the function that governs the underlying time series process. This approach extends naturally to modelling multivariate time series. We show how to estimate the potential function for dimensions one and higher and use it to model statistically the evolution of the time series. An illustration of the procedure shows that testing the resulting model against historical data of oil prices captures the essential price behavior remarkably well. The model allows the generation of copies of the observed time series as well as providing better predictions by reducing uncertainty about the future behavior of the time series.