In this paper, we first study the ARMA model and its derivative models, smooth the non-stationary time series by order difference, and estimate the coefficients of the ARMA model by the method of moment estimation. Then, hypothesis testing is conducted based on serial correlation of the relationship between corporate business administration and organizational effectiveness. In the process of hypothesis testing, the empirical likelihood method is used to test the serial correlation of the residual terms under weak hypotheses, which is then extended to apply to the test case where the residual terms contain finite and infinite variances. Finally, based on the model, we assessed the level of business administration and organizational effectiveness of Enterprise H, explored the correlation between the two, and analyzed the linkage effect between business administration and organizational effectiveness. The results show that there is a significant positive correlation between the dimensions of business administration and organizational effectiveness of enterprises, r=0.754-0.864, P<0.01. The correlation coefficients between the two fluctuate between 0.4 and 0.8 for a long period of time, with significant time-varying characteristics.