We prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. To this end, we revisit this problem for nonparametric autoregressive processes and give some quantitative conditions (i.e., with explicit constants) under which the mixing coefficients...

The paper derives an algorithm for computing leave-k-out diagnostics for the detection of patches of outliers for stationary and non-stationary state space models with regression effects. The algorithm is based on a reverse run of the Kalman filter on the smoothing errors and is both efficient...

Kernel smoothing in nonparametric autoregressive schemes offers a powerful tool in modelling time series. In this paper it is shown that the bootstrap can be used for estimating the distribution of kernel smoothers. This can be done by mimicking the stochastic nature of the whole process in the...