Advancing a holistic theory of networks and network processes requires the extension of existing results in the processing of time-varying signals to signals supported on graphs. This paper focuses on the definition of stationarity and power spectral density for random graph signals, generalizes the concepts of autoregressive and moving average random processes to the graph domain, and investigates their parametric spectral estimation. Theoretical and algorithmic results are complemented with numerical tests on synthetic and real-world graphs.