GPS Time series analysis by Auto Regressive Moving Average (ARMA) technique

The main purpose of this paper is using the probablity models , Auto Regressive Moving Average (ARMA) in order to modeling of daily position time series of permanent GPS station. The daily position time series of LLAS site in Southern California region from SCIGN array that were active during January 1 , 2000 to Dec 30 , 2006 are evaluated for analysis and determinig of daily position time series . According of daily position time series , a site motion model is used to estimate simultaneously geodetic parameters such as : linear trend , annual harmonics , semi annual harmonics and offsets . In each daily position time series, model parameters are estimated using weighted least squares. In this study, Auto Correlation Function ( ACF ) and Partial Auto Correlation Function ( PACF ) are used as study tools for identification of behavior of daily position time series of permanent GPS station . These functions provide consideration of correlations between daily positions of daily time series . Moreover , Akaike Information Criterion is used to identify model orders, because some kind of ARMA model may appropriate for a daily position time series of GPS station. In this study, some numerical results shows that a model order from ( 1 , 1 ) is appropriate for direction N of permanent GPS station . Probabality model of ARMA (2 , 1 ) is best model for direction E and a model order from ( 1 , 1 ) is suitable for direction U. In the final step, a daily position time series of LLAS permanent station were predicted for seasonal component.