Serial correlation test of parametric regression models with response missing at random

It is well-known that successive residuals may be correlated with each other, and serial correlation usually result in an inefficient estimate in time series analysis. In this paper, we investigate the serial correlation test of parametric regression models where the response is missing at random. Three test statistics based on the empirical likelihood method are proposed to test serial correlation. It is proved that three proposed empirical likelihood ratios admit limiting chi-square distribution under the null hypothesis of no serial correlation. The proposed test statistics are simple to calculate and convenient to use, and they can test not only zero first-order serial correlation, but also the higher-order serial correlation. A simulation study and a real data analysis are conducted to evaluate the finite sample performance of our proposed test methods.