Jackknife estimation of stationary autoregressive models

This paper explores the properties of jackknife methods of estimation in stationary autoregressive models. Some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non-overlapping sub-samples are derived for the case of a stationary autoregression of order p when the number of sub-samples is either fixed or increases with the sample size at an appropriate rate. The results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models. This finding is robust to departures from normality, ARCH effects and misspecification. The median-unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife-based confidence intervals.