Electrons with energies >500 keV in the Earth's outer magnetosphere exhibit very hard energy spectra and highly variable absolute intensities. The fluxes often show a strong 27-day periodicity which is related to recurrent solar wind stream variations at 1 AU. We have used available solar wind speed data as well as continuous geomagnetic indices such as Kp and Ae in order to characterize the relationship of relativistic electrons to these geophysical parameters. The present analysis emphasizes data taken in 1982--1985 and employs electron measurements from 3 to 40 MeV at geostationary orbit along with geomagnetic data from the National Geophysical Data Center CD ROM. The method of linear prediction filter (LPF) analysis is used to characterize and predict the general relationship between solar wind or geomagnetic indices as input time series and electron properties as the output time series. Filters are found that generally decrease strongly at zero lag time and then peak strongly at lags of 2--3 days. Cross-covariance analyses show strong correlative peaks between electron fluxes and geomagnetic parameters at multiples of 13 and 27 days. The present analysis allows enhanced understanding of the relativistic electron behavior on both short and long time scales and permits improved prediction of both high-altitude spacecraft operational environments and magnetosphere-atmosphere coupling relationships. ¿ American Geophysical Union 1990