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Licensed Unlicensed Requires Authentication Published by De Gruyter November 14, 2012

Bootstrap, Jackknife and COLS: Bias and Mean Squared Error in Estimation of Autoregressive Models

Gareth D. Liu-Evans and Garry D. A. Phillips

Abstract

We compare a number of bias-correction methodologies in terms of mean squared error and remaining bias, including the residual bootstrap, the relatively unexplored Quenouille jackknife, and methods based on analytical approximation of moments. We introduce a new higher-order jackknife estimator for the AR(1) with constant. Simulation results are presented for four different error structures, including GARCH. We include results for a relatively extreme situation where the errors are highly skewed and leptokurtic. It is argued that the bootstrap and analytical-correction (COLS) approaches are to be favoured overall, though the jackknife methods are the least biased. We find that COLS tends to have the lowest mean squared error, though the bootstrap also does well.

Published Online: 2012-11-14

©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston