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This paper deals with the problem of joint determination of the delay parameter and autoregressive orders of the Self-Exciting Threshold Autoregressive (SETAR) models. More specifically, we propose...

In this article, a new chaotic functional-coefficient nonlinear autoregressive time series model is formulated. Asymptotic stability of the equilibria of the skeleton is studied. Complex dynamics of the proposed model are investigated by means of the bifurcations, time series diagrams, and phase portraits. The effects of noise intensity on its dynamics and the intermittency phenomenon are also discussed via simulation. Two chaotic indicators, namely, the fractal dimension and the Lyapunov exponent methods are investigated for the model.

A monitoring scheme is proposed to sequentially detect a structural change in random coefficient autoregressive time series of order p (RCA(p)) after a training period of size T. It extends structural change monitoring to RCA(p) time series. The asymptotic properties of our monitoring statistic are established under both the null of no change in parameters and the alternative of a change in coefficient. The finite sample properties are investigated by a simulation study.

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVARS(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.

This article is devoted to the study of the periodicity testing problem in a self-exciting threshold autoregressive (SETAR) model. The local asymptotic normality (LAN) property is shown via the adapted sufficient conditions due to Swensen (1985). Moreover, the LAN of the central sequence is established. First, we consider the case where the innovation density is specified and we obtain a parametric local asymptotic test. Second, we construct an adaptive test in the case where this density is unspecified but symmetric. The performances of these established tests are shown via simulation studies.

We define multivariate Self–Exciting Threshold Autoregressive (MSETAR) Models and present an adaptive algorithm for the estimation of the AR coefficients. This algorithm has a similar structure as stochastic gradient procedures (so–called LMS algorithms) which have been frequently used in linear models. It is shown that conditions of convergence known from the linear case can be reformulated for the nonlinear MSETAR model.

This paper uses the local Lyapunov exponent (Wolff (1992)) to show that the dynamics of a chaotic (with and without noise) SETAR(2; l, l)is similar to that of a noisy limit cycle generated from a SETAR(2; 1, 1).

Several estimators of the constant mean about which a stationary first-order autoregressive process varies are studied by utilizing Monte Carlo techniques.