The authors consider a discrete second-order stationary process with slowly decaying autocorrelation function
. It is assumed that
, i.e. the autocorrelations are not absolutely summable. The spectral density function is calculated, which turns out to be unbounded at zero. Several other properties of the process are listed. Among other things the asymptotic behaviour of the eigenvalues of the autocovariance matrix is investigated. In order to obtain an estimator for the parameter
, the maximum likelihood method is applied.