One of the tasks in studies of stochastic regression models or multiparameter statistic inference problems is to find sufficient conditions for the strong law of large numbers for multivariate martingales with random norming. For that purpose, we give a weaker sufficient condition for the random...

We examine a kernel regression smoother for time series that takes account of the error correlation structure as proposed by Xiao et al. (2008). We show that this method continues to improve estimation in the case where the regressor is a unit root or near unit root process.

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...

We examine a kernel regression smoother for time series that takes account of the error correlation structure as proposed by Xiao et al. (2008). We show that this method continues to improve estimation in the case where the regressor is a unit root or near unit root process

We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly...

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical...

We consider nonparametric estimation of the regression function g(*) in a nonlinear regression model Y_t = g(X_t) o(X_t)e_t, where the regressor X_t is a nonstationary unit root process and the error e_t is s sequence of independent and identically distributed (i.i.d.) random variables. With proper...

Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale...

This paper develops an asymptotic theory for near-integrated random processes and some associated regressions when the errors are tempered linear processes. Tempered processes are stationary time series that have a semi-long memory property in the sense that the autocovariogram of the process...