Abstract We consider d-order Markov chains satisfying a conditional constraint E(aθ(Xi−1, Xi) | Xi−1) = 0, where Xi−1 = (Xi−1, . . . , Xi−d). These comprise quasi-likelihood models and nonlinear and conditionally heteroscedastic autoregressive models with martingale innovations. Estimators for θ can be obtained from estimating equations ∑n i=1Wθ(Xi−1) aθ(Xi−1, Xi) = 0. We review different crite...

Linearized stability analysis methodologies that are applicable to general nonlinear rotorcraft problems are presented in this paper. Two classes of closely related algorithms, based on a partial Floquet and an autoregressive approach, are presented in a common framework that underlines their similarity and their relationship to other methods. The robustness of the proposed approach is improved...

In this article we propose a test for additivity of a nonlinear conditionally heteroscedastic autoregressive model. A test is based on the unequal variance unbalanced design ANOVA scheme. Asymptotic distribution of the test statistic is derived and the test performance in finite samples is studied using simulation. To the best of our knowledge, this is the first additivity test for a conditiona...

We consider a non-homogeneous nonlinear stochastic difference equation Xn+1 = Xn (

We examine dynamic asymmetries in U.S unemployment using nonlinear time series models and Bayesian methods. We nd strong statistical evidence in favor of a two-regime threshold autoregressive model. Empirical results indicate that, once we take into account both parameter and model uncertainty, there are economically interesting asymmetries in the unemployment rate. One nding of particular inte...

Consider a stochastic difference equation xi+1 = Gi [xi, xi−1, . . . , x0] + fi [xi, xi−1, . . . , x0] + k0 ∑ k=0 σi−k [xi−k, xi−k−1, . . . , x0] ξi+1−k, (1) with the Volterra type nonlinear main term G and the Volterra type noise f + ∑k0 k=0 σi−kξi+1−k. Functions Gi, fi, σi are random while ξi is a martingale-difference. In general, k0 ≥ 1 so Eqn (1) cannot be considered as a stochastic equati...

Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear model are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of model. Finally forecasting and impul...

The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the VARMA models, and allows to cover linear representations of general nonlinear ...

Price dynamics for North American oriented strand board markets are examined. The role of transactions costs are explored vis-à-vis the law of one price. Nonlinearities induced by unobservable transactions costs are modeled by estimating time-varying smooth transition autoregressions (TV-STARs). Results indicate that nonlinearity and structural change are important features of these markets; pr...

An intensive nonlinear analysis of geomagnetic time series from the magnetic network on Etna volcano was carried out to investigate the dynamical behavior of magnetic anomalies in volcanic areas. The short-term predictability of the geomagnetic time series was evaluated to establish a possible low-dimensional deterministic dynamics. We estimated the predictive ability of both a nonlinear foreca...