Parameter Estimation For Nonlinear Time-Series Models

Time-series analysis and modeling are helpful to understand random dynamic systems,predict future events and control them through intervention.Although linear timeseries models have been widely applied in finance,biology,hydrology and other fields,it may result in information loss and poor effect when using linear models to approximate some nonlinear characteristics in practice.Thus,nonlinear time-series modeling is an important research topic.This academic dissertation investigates the parameter estimation algorithms for a class of nonlinear time-series models.The main research contents are as follows.1.For the classic nonlinear exponential autoregressive(Exp AR)time-series model,the corresponding estimation is a highly nonlinear optimization problem.When using the gradient search to solve this optimization problem,the algebraic solution of the optimal step-size cannot be obtained.This dissertation presents a new approach of determining the step-size by applying the first-order Taylor expansion approximation.Based on the resulting optimal step-size,the stochastic gradient algorithm is proposed to estimate all the unknown parameters.To improve the data utilization and parameter estimation accuracy,the multi-innovation stochastic gradient algorithm is proposed through the innovation expansion.2.For the classic nonlinear Exp AR time-series model,the multi-innovation Newton recursive algorithm is proposed by applying the stacked data and Newton search,such that all the unknown parameters can be estimated simultaneously.To enhance the computational efficiency,the identification model is decomposed into two subidentification(Sub-ID)models by using the hierarchical principle,which respectively contains the unknown parameters of the linear and nonlinear part of the original model.Based on the Newton search,the parameter estimation sub-algorithms for these two Sub-ID models are derived.Then,by coordinating the associate terms of the Sub-ID models,the decomposition-based multi-innovation Newton recursive algorithm is proposed to interactively estimate these two sets of parameters.3.For the Exp AR moving average(Exp ARMA)time-series model,to reduce the effect of the colored noise,a linear filter is designed to filter the measurements by using the data filtering technique.Combining with the gradient search and innovation expansion,the filtering-based multi-innovation extended stochastic gradient algorithm is proposed. Under the framework of the data filtering,by exploiting the hierarchical principle,the filtered identification model is decomposed into two Sub-ID models,and the filteringbased three-stage multi-innovation extended stochastic gradient algorithm is proposed to reduce the scale and complexity of the estimation problem.4.For the time-delay Exp AR time-series model,the identification model is expanded into an augmented one by employing the redundant rule.To avoid the effect of the threshold in traditional algorithms on the estimation accuracy,by defining an energy coefficient cost function,the estimation problem is transferred into a new optimization problem.Combining with the innovation expansion,the redundant rulebased multi-innovation stochastic gradient algorithm is proposed.For the time-delay Exp ARMA model,the data filtering technique is used to propose the redundant rulebased filtering multi-innovation extended stochastic gradient algorithm,such that the unknown parameters and time-delay can be jointly estimated.In summary,this academic dissertation investigates the parameter estimation problems for nonlinear time-series models,whose structures are from simple to complex.Detailed derivation and pseudo-codes for all the proposed algorithms are provided,and simulation examples are used to verify and compare the effectiveness of the proposed algorithms.