Bootstrap with larger resample size for root-n consistent density estimation with time series data

We consider finite-order moving average and nonlinear autoregressive processes with no parametric assumption on the error distribution, and present a kernel density estimator of a bootstrap series that estimates their marginal densities root-n consistently. This is equal to the rate of the best known convolution estimators, and is faster than the standard kernel density estimator. We also conduct simulations to check the finite sample properties of our estimator, and the results are generally better than corresponding results for the standard kernel density estimator.