A cusum test in the linear regression model with serially correlated disturbances
研究了Dufour(1982)提出的修正CUSUM检验，用于检测线性回归模型中参数不稳定和结构变化，推导了该检验在序列相关扰动下的渐近分布，并证明其与无序列相关时的CUSUM检验具有相同的渐近分布。
This paper considers a modified CUSUM test, suggested by Dufour (1982) for parameter instability and structural change with an unknown change point in a linear model with serially correlated disturbances, in which a preliminary estimate of the autoregressive coefficient for the error process is obtained, and used to transform the data. Then the standard CUSUM statistic is calculated on the transformed data. This paper derives the asymptotic distribution of the modified CUSUM test. We show that the modified CUSUM test retains its asymptotic significance level, i.e., the modified CUSUM test has the same asymptotic distribution as the CUSUM test with serially uncorrelated errors.