A Note on the Selection of Time Series Models
研究使用信息准则选择自回归模型阶数时，有效观测数、方差估计的自由度调整以及过拟合惩罚定义方式对估计结果的影响，并通过模拟和理论分析提供稳健模型选择的指南。
Abstract We consider issues related to the order of an autoregression selected using information criteria. We study the sensitivity of the estimated order to (i) whether the effective number of observations is held fixed when estimating models of different order, (ii) whether the estimate of the variance is adjusted for degrees of freedom, and (iii) how the penalty for overfitting is defined in relation to the total sample size. Simulations show that the lag length selected by both the Akaike and the Schwarz information criteria are sensitive to these parameters in finite samples. The methods that give the most precise estimates are those that hold the effective sample size fixed across models to be compared. Theoretical considerations reveal that this is indeed necessary for valid model comparisons. Guides to robust model selection are provided.