For functional time series data with α-mixed structure when the response variables are randomly missing the functional single indicator model is used for statistical modeling and the k-nearest neighbor method is used to estimate the unknown parameters and unknown functions in the model. Compared with the classical kernel method the method proposed in this paper has better data applicability and can improve the estimation efficiency. The k-nearest neighbor method was compared with the classical kernel method through numerical simulations and El Ni?o sea level temperature data to discuss the estimation effects of the k-nearest neighbor method and the classical kernel method on the unknown parameters and unknown functions. From the simulation results it can be seen that the k-nearest neighbor method outperformed the classical kernel method in terms of accuracy of estimation of unknown parameters and unknown functions as well as improvement with increasing samples. Moreover in the analysis of real data the k-nearest neighbor method performed well in the accuracy fitting and trend fitting of real data. These results show that the k-nearest neighbor method is superior to the classical kernel method in terms of accuracy in estimating the unknown parameters and unknown functions in a single indicator model of a time series with random missing response variables. Meanwhile in the real data analysis the k-nearest neighbor method can better fit the data than the classical kernel method.