Identification of model order and number of neighbors for k-nearest neighbor resampling

Among the various stochastic models used in hydrology and meteorology, the k-nearest neighbor resampling (KNNR) has been one of the most common alternatives to supplement the short historical records. In the KNNR model one needs to select the model order (d) and the number of nearest neighbors (k). Traditionally, the prescriptive selection (k = n1/2 where n is the record length) has been used for k and no practical solutions were provided to choose d. Another applicable approach is generalized cross-validation (GCV). However, it has been reported in the literature that GCV is not practical for the selection of d and k in the KNNR model. In the current study we propose an approach to select d and k based on the Akaike information criterion (AIC). The proposed approach was validated on a number of simulated datasets and applied to the case study of the Colorado River system. The results indicate that the proposed AIC-based approach represents a robust model for the selection of d and k. In the simulation study, the model led particularly to the selection of the same model orders as the real orders of the simulated datasets. It also gave acceptable k values in the case study.