Recovering of Gaps in Multivariate Time Series Using Methods of Mathematical Statistics and Machine Learning

Abstract

The research focuses on multivariate time series of geophysical parameters. During the study, statistical and machine learning methods were employed to recover missing data. The following results were achieved: for the CO\({}_{2}\) concentration series at a height of 30 m, the ARIMAX model demonstrated the lowest RMSE and MAE metrics, taking only 2.3 s for recovery, which is significantly faster compared to the LSTM (251 s) and GRU (160 s) neural network models. Recovery of air–temperature data was performed most effectively using the recurrent neural network GRU. The results indicate that ARIMA family models are more suitable for data recovery when correlated parameters are present, whereas GRU-based neural networks are preferable in other cases. The conclusions can be used to improve data recovery methods in multivariate time series.