Application of the ARIMA model to analyze and forecast the time series of density corrections for NRLMSIS-00
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Previously the authors described a technique for estimating the fluctuations between the actual atmosphere density and a chosen atmosphere density model. The observation data is the Two Line Element set data associated with catalogued inactive payloads and debris. Time-series for the density corrections for the Russian operational GOST atmosphere density model and for the US NRLMSIS-00 atmosphere density model were constructed over a four-year interval. In this paper, the authors investigate the basic statistical properties of the observed density corrections for the NRLMSIS-00 model. The following are provided: - Statistical distributions of the b 1 and b 2 density correction coefficient time series along with distributions of the solar activity and the geomagnetic index - Correlations (with scatterplots) between the b 1 and b 2 time series, as well as with the solar activity and the geomagnetic index time series - Autocorrelation functions for the b 1 and b 2 time series, and the solar activity and the geomagnetic index time series, for various lag times - Cross correlation functions These results suggest that time series analysis techniques may be applied to identify the nature of the phenomena represented by the time series of the density correction estimates and for their forecasting. The matrix autoregression equations for the parameters of the density corrections are constructed in order to reveal the time regularities of the density correction parameters, and to allow more efficient prediction of the density correction parameters. The Autoregressive Integrated Moving Average (ARIMA) method is used to construct simple scalar models describing the b 1 and b 2 time series of density corrections for the NRLMSIS-00, to smooth them, and to predict the future values of the time series using observations up to the current time. The ARIMA model represents the time series values observed at the given time instant as a linear combination of previous values of the series and a linear combination of moving averages. The ARIMA methodology was developed by Box and Jenkins. It has gained enormous popularity in many areas of research. The selection of the ARIMA model parameters, which adequately describe the behavior of the analyzed b 1 and b 2 time series of density corrections, was carried out by enumerating a set of test models. The accuracy of the density correction forecasting for the NRLMSIS-00 model was estimated using an ARIMA (6,1,6) model.