ASYMPTOTIC THEORY FOR THE DURBIN–WATSON STATISTIC UNDER LONG-MEMORY DEPENDENCE
研究了时间序列回归模型中残差为长记忆过程时，德宾-沃森统计量的渐近性质，提出了标准化统计量并推导其渐近分布和局部检验功效，对计量经济学和统计学者有参考价值。
In time series regression models with “short-memory” residual processes, the Durbin–Watson statistic ( DW ) has been used for the problem of testing for independence of the residuals. In this paper we elucidate the asymptotics of DW for “long-memory” residual processes. A standardized Durbin–Watson statistic ( SDW ) is proposed. Then we derive the asymptotic distributions of SDW under both the null and local alternative hypotheses. Based on this result we evaluate the local power of SDW . Numerical studies for DW and SDW are given.