On partial-sum processes of ARMAX residuals
研究了ARMAX模型残差的部分和过程的极限行为，给出了多种情形下的极限分布，并提供了用于CUSUM检验的枢轴统计算法，对时间序列建模和检验有参考价值。
We establish general and versatile results regarding the limit behavior of the partial-sum process of ARMAX residuals. Illustrations include ARMA with seasonal dummies, misspecified ARMAX models with autocorrelated errors, nonlinear ARMAX models, ARMA with a structural break, a wide range of ARMAX models with infinite-variance errors, weak GARCH models and the consistency of kernel estimation of the density of ARMAX errors. Our results identify the limit distributions, and provide a general algorithm to obtain pivot statistics for CUSUM tests.