A Note on Bootstrapping M‐Estimators in ARMA Models

Michael Allen and Somnath Datta

Journal of Time Series Analysis, 1999, vol. 20, issue 4, 365-379

Abstract: Kreiss and Franke (Bootstrapping stationary autoregressive moving‐average models. J. Time Ser. Anal.13 (1992), 297–317) proposed bootstrapping a linear approximation to the M‐estimator in autoregressive moving‐average (ARMA) models. In this paper, it is argued that it may be better to apply the bootstrap principle directly to the M‐estimator itself. A number of simulation results are presented to compare the two procedures for estimating the sampling distribution of an M‐estimator. The theoretical asymptotic validity of the standard bootstrap applied to the M‐estimator is established.

Date: 1999
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