Consistent Order Determination for Processes with Infinite Variance
研究了当残差服从无限方差稳定律时，自回归和移动平均过程的阶数确定方法，证明了FPEα准则和基于逆相关估计的程序能一致估计阶数，并通过模拟验证了有限样本表现。
SUMMARY Order determination for autoregressive processes when the residuals have a distribution belonging to the domain of attraction of an infinite variance stable law is examined. The use of the FPEα criterion of Bhansali and Downham (1977) is shown to provide a consistent estimator of the order with any α > 0. Order determination for moving average processes is considered; a procedure based on autoregressive estimates of the inverse correlations, see Bhansali (1983), is shown to provide a consistent estimator of the order. Consistency of the estimated autoregressive and moving average parameters of an arbitrary order is established. The question of consistent discrimination between autoregressive and moving average models is also considered. The finite sample behaviour of the discrimination procedure is investigated by means of a simulation study.