The application of the time series theory to processing data from the SBAS receiver with safety of life service

Before satellite-based augmentation systems (SBAS) such as the Wide Area Augmentation System (WAAS) in the USA, and the European Geostationary Navigation Overlay Service (EGNOS), will be used in railway safety-related applications, it is necessary to determine reliability attributes of these systems as quality measures from the user´s point of view. It is necessary to find new methods of processing data from the SBAS system in accordance with strict railway standards. For this purposes data from the SBAS receiver with the Safety of Life service was processed by means of the time series theory. At first, a basic statistic exploration analysis by means of histograms and box plot graphs was done. Then correlation analysis by autocorrelation (ACF), and partial autocorrelation functions (P ACF), was done. Statistical tests for the confirmation of nonstationarity, and conditional heteroscedasticity of time series were done. Engle´s ARCH test confirmed that conditional heteroscedasticity is contained. ARMA/GARCH models were constructed, and their residuals were analyzed. Autocorrelation functions and statistical tests of models residuals were done. The analysis implies that the models well cover the variance volatility of investigated time series and so it is possible to use the ARMA/GARCH models for the modeling of SBAS receiver outputs.