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Higher-Order Improvements Of The Parametric Bootstrap For Markov Processes, Donald W.K. Andrews
Higher-Order Improvements Of The Parametric Bootstrap For Markov Processes, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper provides bounds on the errors in coverage probabilities of maximum likelihood-based, percentile- t , parametric bootstrap confidence intervals for Markov time series processes. These bounds show that the parametric bootstrap for Markov time series provides higher-order improvements (over confidence intervals based on first order asymptotics) that are comparable to those obtained by the parametric and nonparametric bootstrap for iid data and are better than those obtained by the block bootstrap for time series. Additional results are given for Wald-based confidence regions. The paper also shows that k -step parametric bootstrap confidence intervals achieve the same higher-order improvements as …
Second Order Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter, Offer Lieberman, Peter C.B. Phillips
Second Order Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter, Offer Lieberman, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0, d ,0) model is well known to be asymptotically N (0, 6/ π 2 ). This paper develops a second order asymptotic expansion to the distribution of this statistic. The correction term for the density is shown to be independent of d , so that the MLE is second order pivotal for d . This feature of the MLE is unusual, at least in time series contexts. Simulations show that the normal approximation is poor and that the expansions make significant improvements in accuracy.