In this paper, we introduce a new class of bivariate threshold VAR cointegration models. In the models, outside a compact region, the processes are cointegrated, while in the compact region, we allow different kinds of possibilities. We show that the bivariate processes from a 1/2-null recurrent...

This paper discusses nonparametric kernel regression with the regressor being a \(d\)-dimensional \(\beta\)-null recurrent process in presence of conditional heteroscedasticity. We show that the mean function estimator is consistent with convergence rate \(\sqrt{n(T)h^{d}}\), where \(n(T)\) is...

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...

This paper considers a general model specification test for nonlinear multivariate cointegrating regressions where the regressor consists of a univariate integrated time series and a vector of stationary time series. The regressors and the errors are generated from the same innovations, so that...

Estimation in two classes of popular models, single-index models and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link function in the models and a profile approach...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...

This paper establishes several results for uniform convergence of nonparametric kernel density and regression estimates for the case where the time series regressors concerned are nonstationary null–recurrent Markov chains. Under suitable conditions, certain rates of convergence are also...

This paper proposes a class of new nonlinear threshold autoregressive models with both stationary and nonstationary regimes. Existing literature basically focuses on testing for a unit–root structure in a threshold autoregressive model. Under the null hypothesis, the model reduces to a...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...