In recent years, there has been increasing interest in nonparametric bootst
rap inference for economic time series. Nonparametric resampling techniques
help protect against overly optimistic inference in time series models of
unknown structure. They are particularly useful for evaluating the fit of d
ynamic economic models in terms of their spectra, impulse responses, and re
lated statistics because they do not require a correctly specified economic
model. Notwithstanding the potential advantages of nonparametric bootstrap
methods, their reliability in small samples is questionable. In this paper
, we provide a benchmark for the relative accuracy of several nonparametric
resampling algorithms based on ARMA representations of four macroeconomic
time series. For each algorithm, we evaluate the effective coverage accurac
y of impulse response and spectral density bootstrap confidence intervals f
or standard sample sizes. We find that the autoregressive sieve approach ba
sed on the encompassing model is most accurate. However, care must be exerc
ised in selecting the lag order of the autoregressive approximation.