Accounting for Lag Order Uncertainty in Autoregressions: the Endogenous Lag Order Bootstrap Algorithm

Lutz Kilian

Journal of Time Series Analysis, 1998, vol. 19, issue 5, 531-548

Abstract: Conventional asymptotic and bootstrap methods for finite‐order autoregressive models condition on the estimated lag order of the model as though it were known to be the true lag order. Even if the order is estimated correctly, this procedure ignores the sampling uncertainty about the lag order estimate and may result in spurious inferences. In this paper an appropriately modified bootstrap algorithm is introduced that reflects the true extent of sampling uncertainty in the regression estimates. This endogenous lag order bootstrap algorithm recognizes that lag order selection is an integral part of the sampling procedure by re‐estimating the lag order in each bootstrap iteration. It is suggested that the endogenous lag order bootstrap algorithm should routinely replace the standard bootstrap algorithm in applications. Monte Carlo simulations show that ignoring lag order uncertainty may seriously undermine the coverage accuracy of bootstrap confidence intervals for vector autoregression impulse response estimates. Endogenizing the lag order choice is shown to improve coverage accuracy in small samples at negligible additional computational cost. As the lag order uncertainty declines in large samples, the performance of the endogenous lag order interval converges to that of the standard interval.

Date: 1998
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