A Flexible Coefficient Smooth Transition Time Series Model

Abstract

In this paper, we consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the self-exciting threshold autoregressive (SETAR), the autoregressive neural network (AR-NN), and the logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel measurable function, our formulation is directly comparable to the functional coefficient autoregressive (FAR) and the single-index coefficient regression models. A model building procedure is developed based on statistical inference arguments. A Monte Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.

Testing for Heteroskedasticity of the Residuals in Fuzzy Rule-Based Models

“…It has been proved [1] that this specification of the FRBM nests some models from the autoregressive regime switching family. More precisely, it is closely related with the Threshold Autoregressive model (TAR) [12], the Smooth Transition Autoregressive model (STAR) [11], the Linear Local-Global Neural Network (L 2 GNN) [10] and the Neuro-Coefficient STAR [9]. This relation has given place to an ongoing exchange of knowledge and methods from the statistical framework to the fuzzy rule-based modelling of time series.…”

“…The sigmoid function is the one used in [9], and although it is not so common in the fuzzy literature, we will use it here as an immediate result derived from the equivalences stated in [?]. As we know, it is defined as…”

Moment-based estimation of smooth transition regression models with endogenous variables

“…However, under stationarity or cross-section applications, the covariates have been assumed to be weakly exogeneous with respect to the parameters of interest. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares, and the asymptotic properties of the estimators have been discussed in Mira and Escribano (2000), Suarez-Fariñas, Pedreira, and Medeiros (2004), and Medeiros and Veiga (2005), among others. Nonlinear least squares is equivalent to quasi-maximum likelihood or, when the errors are Gaussian, to conditional maximum likelihood.…”

Automated Linear Modeling of Time Series with Self Adaptive Genetic Algorithms

“…The most classical reference for the treatment of linear models is [3]. Additionally, other methodologies use them to make forecasts [4], [15], [16] First of all, the problem in finding a good linear model for a series of data is that it requires the determination of how many and which terms are the most appropriate to solve this problem. Secondly, it is necessary to know in which intervals the coefficients of the linear expression are, and finally, to find the values for these coefficients that minimize the quadratic error for the whole history.…”