This paper studies functional coefficient regression models with nonstationary time series data, allowing also for stationary covariates. A local linear fitting scheme is developed to estimate the coefficient functions. The asymptotic distributions of the estimators are obtained, showing...

Due to nonstationary (nearly integrated or integrated) regressors and the embedded endogeneity, a linear predictive regression model produces biased coefficient estimates, which consequentially leads to the conventional t-test to over-reject the misspecification test. In this paper, our aim is...

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of...

We study quantile regression estimation for dynamic models with partially varying coefficients so that the values of some coefficients may be functions of informative covariates. Estimation of both parametric and nonparametric functional coefficients are proposed. In particular, we propose a...

We provide a new asymptotic analysis of model selection procedure that compares likelihoods of two candidate diffusion models. Our asymptotic analysis relies on two dimensional asymptotic expansions with shrinking sampling interval Δ and increasing sampling span T, and clarifies the different...

We analyze in this paper the asymptotic behavior of the specification test of Aït-Sahalia (1996) for the stationary density of a diffusion process, but when the diffusion is not stationary. We consider integrated and explosive processes, as well as nearly integrated ones in the spirit of the...

A formal test on the Lyapunov exponent is developed to distinguish a random walk model from a chaotic system, which is based on the Nadaraya–Watson kernel estimator of the Lyapunov exponent. The asymptotic null distribution of our test statistic is free of nuisance parameter, and simply given...

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of...