The Analysis of Stationary Processes with Mixed Spectra—I

SUMMARY We consider a normal stationary process whose spectrum may contain harmonic components superimposed on a non-uniform continuous spectral density function. The problem of separating the discrete and continuous spectral components is discussed, and it is shown that the bandwidth of the spectral density function must be restricted, in relation to the number of observations, in order to make the problem tractable. Assuming only that this bandwidth is known, the presence of harmonic components is then detected by performing a “spectral” analysis on the tail of the autocovariance function, and a test is constructed based on the theory of random walks with absorbing barriers. A brief discussion of the case of non-normal processes is included.