We develop optimal formulations for nonlinear autoregressive models by representing them as linear autoregressive models with time-varying temporal dependence coefficients. We propose a parameter updating scheme based on the score of the predictive likelihood function at each time point. The...

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...

We provide a limit theory for a general class of kernel smoothed U statistics that may be used for specification testing in time series regression with nonstationary data. The framework allows for linear and nonlinear models of cointegration and regressors that have autoregressive unit roots or...

This paper considers a nonlinear time series model associated with both nonstationarity and endogeneity. The proposed model is then estimated by a nonparametric series method. An asymptotic theory is established in both point-wise and the space metric sense for the estimator. The Monte Carlo...

This paper discusses nonparametric series estimation of integrable cointegration models using Hermite functions. We establish the uniform consistency and asymptotic normality of the series estimator. The Monte Carlo simulation results show that the performance of the estimator is numerically...

We propose two robust bootstrap-based simultaneous inference methods for time series models featuring time-varying coefficients and conduct an extensive simulation study to assess their performance. Our exploration covers a wide range of scenarios, encompassing serially correlated,...

This article suggests and compares the properties of some nonlinear Markov-switching filters. Two of them are sigma point filters: the Markov switching central difference Kalman filter (MSCDKF) and MSCDKFA. Two of them are Gaussian assumed filters: Markov switching quadratic Kalman filter...

Exponential smooth transition autoregressive (ESTAR) models are widely used in the international finance literature, particularly for the modelling of real exchange rates. We show that the exponential function is ill-suited as a regime weighting function because of two undesirable properties....

We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identifed. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal...

This article proposes omnibus specification tests of parametric dynamic quantile regression models. Contrary to the existing procedures, we allow for a flexible and general specification framework where a possibly continuum of quantiles are simultaneously specified. This is the case for many...