Hybrid Fourier–ARIMA Approach for Forecasting Time Series of Permanent GNSS Stations

Abstract

The modern era can be characterized as a data-driven age, in which advanced analytical techniques and artificial intelligence methods rely on the processing of large datasets to identify underlying patterns and relationships. In the field of geodesy, numerous applications involve the analysis of time series, including temperature variations, global mean sea level rise, Earth's polar motion, and coordinate variations of permanent GNSS stations, all of which contribute to a better understanding of the Earth's shape and geodynamic processes. This study presents a hybrid approach for forecasting time series using data from a permanent GNSS station as a case study. The novelty of the proposed methodology lies in a two-stage processing strategy. In the first stage, the deterministic periodic component is identified and removed using a truncated Fourier series representation, and the resulting residual series is tested for stationarity using autocorrelation (ACF) and partial autocorrelation (PACF) functions. In the second stage, the residual component is modeled and forecasted using an autoregressive integrated moving average (ARIMA) model, with particular emphasis placed on the identification of the optimal model parameters (p, d, q). All computational results are supported by graphical representations and summarized in tabular form. The proposed approach demonstrates good predictive performance, with the standard deviation of the differences between predicted and observed values equal to 4.5 mm.