A Bootstrap Variant of Aic for State-space Model Selection

Following in the recent work of Hurvich and Tsai (1989, 1991, 1993) and Hurvich, Shumway, and Tsai (1990), we propose a corrected variant of AIC developed for the purpose of small-sample state-space model selection. Our variant of AIC utilizes bootstrapping in the state-space framework (Stoffer and Wall (1991)) to provide an estimate of the expected Kullback-Leibler discrepancy between the model generating the data and a fitted approximating model. We present simulation results which demonstrate that in small-sample settings, our criterion estimates the expected discrepancy with less bias than traditional AIC and certain other competitors. As a result, our AIC variant serves as an effective tool for selecting a model of appropriate dimension. We present an asymptotic justification for our criterion in the Appendix.