CONSISTENT DENSITY ESTIMATORS; CONTINUOUS-TIME MODELS; TERM STRUCTURE; DIFFUSION-PROCESSES; LIMIT-THEOREMS; ARCH(1) ERRORS; INTEREST-RATES; SERIES; INFERENCE; VARIABLES
CAMBRIDGE UNIV PRESS
ECONOMETRIC THEORY, v. 31, NO 5, Page. 1078-1101
The paper considers testing parametric assumptions on the conditional mean and variance functions for nonlinear autoregressive models. To this end, we compare the kernel density estimate of the marginal density of the process with a convolution-type density estimate. It is shown that, interestingly, the latter estimate has a parametric (root n) rate of convergence, thus substantially improving the classical kernel density estimates whose rates of convergence are much inferior. Our results are confirmed by a simulation study for threshold autoregressive processes and autoregressive conditional heteroskedastic processes.