Local average of nearest neighbors: Univariate time series imputation

Abstract

The imputation of time series is one of the most important tasks in the homogenization process, the quality and precision of this process will directly influence the accuracy of the time series predictions. This paper proposes two simple algorithms, but quite powerful for univariate time series imputation process, which are based on the means of the nearest neighbors for the imputation of missing data. The first of them Local Average of Neighbors Neighbors (LANN) calculates the missing value from the average of the previous neighbor and the following neighbor to the missing value. The second Local Average of Neighbors Neighbors+ (LANN+), considers a threshold parameter, which allows to differentiate the calculation of the missing values according to the difference between the neighbors: for the differences less than or equal to the threshold the missing value is calculated through of LANN and for major differences the missing value is calculated from the average of the four closest neighbors, two previous and two subsequent to the missing value. Imputation results on different time series are promising.