On Student’s-t ARMA Modelling of Missing Values

In this paper, the study intends to mitigate the missing problem in the context of univariate ARMA time series models. Our main objective of this paper was to derive imputation estimators for ARMA models under the student’s-t distribution assumptions and evaluate their imputation performance. The study also utilized the method of optimal interpolation criterion of missing values to build the novel imputation estimators for ARMA models. A data set of 1000 samples were generated using statistical R software. One hundred (100) points of missing values ware created within the generated sample data at a random mechanism. The study carried out an imputation of missing values using the developed estimators for ARMA (1,1) and ARMA (1,2) processes. In this study, it was evident that the estimators ARMA (1,2) did imputed the missing values better than those of ARMA (1,1) process. This was indicated by lower values of the calculated metrics of ARMA (1,2) compared to those of ARMA (1,1). Besides the development of the imputation estimators, the study did a comparison of the derived imputation estimators of time series with the convectional imputation techniques of missing values. They included K-Nearest Neighbors (KNN), Artificial Neural Networks (ANN) and Kalman filters imputations. The results obtained from the calculated metrics, compared the results of the simulation study that the ANN, KNN and the Kalman filters were better in imputing missing values in time series data. The proposed estimated models of ARMA also did compete well with the convectional techniques used in this study. The models that the study came up with can be of importance to data scientists, researchers in refilling missing data in time series contexts.