Exponential Autoregressive Model Research Articles

A complex nonlinear exponential autoregressive model approach to shape recognition using neural networks

A complex nonlinear exponential autoregressive (CNEAR) process which models the boundary coordinate sequence for invariant feature extraction to recognize arbitrary shapes on a plane is presented. A neural network structure is constructed to calculate all the CNEAR coefficients synchronically. The network is simple in structure and easy to implement. The nonlinear parameter is easy to determine using the network. The coefficients are adopted to constitute the feature set. They are proven to be invariant to the transformation of a boundary such as translation, rotation, scale, and choice of the starting point in tracing the boundary. Afterwards, the feature set is used as the input to a complex multilayer perceptron (C-MLP) network for learning and classification. Experimental results show that complicated shapes can be recognized with high accuracy, even in the low-order models. It is also seen that the CNEAR model performs better than the complex autoregressive (CAR) model when shapes have random noise on the boundaries or have differentiating features at detailed levels. Finally, an extended training scheme is developed in which the network is gradually retrained sequentially with shapes containing small increments of noise to improve the robustness of the C-MLP classifier.

Nonlinear time series modelling with the radial basis function-based state-dependent autoregressive model

This paper investigates nonlinear time series modelling using the general state-dependent autoregressive model. To achieve the estimate of the model, an attempt is made to approximate the state-dependent parameter by employing the Gaussian radial basis function for its universal approximation capability. As a result, a radial basis function-based autoregressive (RBF-AR) model is derived which has a form similar to a generalized exponential autoregressive model. To reach the applicability of the RBF-AR model, the evolutionary programming algorithm is employed to select a suitable set of radial basis function centres. By applying the resulting model to some complex data, it is shown that the RBF-AR model can not only reconstruct the dynamics of given nonlinear time series effectively, but also give much better fitting to complextime series than the approach of directly RBF neural network modelling. Therefore, as a paradigm combining a statistical model and neural network, the RBF-AR model has better performance than the RBF neural network especially for its problem reduction of the curse of dimensionality which is usually regarded as one of the potential main difficulties of RBF neural network modelling.

Identification of the Self-Organizing Exponential Autoregressive Models

Abstract A kind of time series model, namely exponential autoregressive that has properties similar to those of nonlinear random vibrations, is achieved to be identified in self-organization. This paper introduces the genetic algorithm hybridized with the recursive least squares method to select the optimum exponential autoregressive model. The final model identified by this evolutionary approach may be not only a full exponential autoregressive model but also a subset model. The simulations of artificial time series and applications to machine tool chatter analysis are given to show the efficiency of the approach proposed.

Mathematical modelling of nonlinear behaviour of seismicity

In this paper, the nonlinear behaviour of seismic activities has been studied by means of the threshold autoregressive model and the exponential autoregressive model. The contents are as follows: (1) The theories and modelling methods of this two models have been studied. (2) One kind of explanation for the seismic cycle and order structure are given by means of the threshold autoregressive model. (3) According to the exponential autoregressive model, an inherent structure of the magnitude series are discussed, the different relations between magnitude and frequency in active period and quiet period are also explained in this paper.

Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models

Abstract This article considers the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) autoregressive models. This includes the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models are discussed. Estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model. The proposed techniques are illustrated by examples using both simulated and real time series.

A Bivariate First-Order Autoregressive Time Series Model in Exponential Variables (BEAR(1))

A simple time series model for bivariate exponential variables having first-order autoregressive structure is presented, the BEAR(1) model. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR(2)). The process is Markovian in the bivariate sense and has correlation structure analogous to that of the Gaussian AR(1) bivariate time series model. The model exhibits a full range of positive correlations and cross-correlations. With some modification in either the innovation or the random coefficients, the model admits some negative values for the cross-correlations. The marginal processes are shown to have correlation structure of ARMA(2, 1) models.

STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSIS

Abstract. We construct a general class of non‐linear models, called ‘state‐dependent models’, which have a very flexible non‐linear structure and which contain, as special cases, bilinear, threshold autoregressive, and exponential autoregressive models. We describe a sequential type of recursive algorithm for identifying state‐dependent models, and show how such models may be used for forecasting and for indicating specific types of non‐linear behaviour.