This paper studies the statistical properties of a two-step conditional quantile estimator in nonlinear time series models with unspecified error distribution. The asymptotic distribution of the quasi-maximum likelihood estimators and the filtered empirical percentiles is derived. Three...

We develop new tail-trimmed QML estimators for nonlinear GARCH models with possibly heavy tailed errors. Tail-trimming allows both identification of the true parameter and asymptotic normality. In heavy tailed cases the rate of convergence is below but arbitrarily close to root-n, the highest...

This paper establishes two simple and new specification tests based on the use of an orthogonal series. The paper then establishes an asymptotic theory for each of the proposed tests. The first test is initially proposed for the case where the regression function involved is integrable and the...

This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models in which we assume a stochastic autoregressive coefficient depending on the first lagged value of the process itself. We call such a model...

The asymptotic theory for the memory parameter estimator constructed from log-regression with wavelets is incomplete for 1/f processes that are not necessarily Gaussian or linear. Such a theory is needed due to the importance of non-Gaussian and nonlinear long memory models in describing...

Exponential smooth transition autoregressive (ESTAR) models have been widely used in the empirical international finance literature. We show that the exponential function used in ESTAR models is ill-suited as a regime weighting function because of two undesirable properties. The first is that it...