The Averaged Periodogram for Nonstationary Vector Time Series

Frequency domain statistics are studied in the presence of fractional deterministic and stochastic trends. It is shown how the behaviour of the sample variance–covariance matrix of nonstationary processes can be dominated by components corresponding to a possibly degenerating band around zero frequency. This property is used to establish the limiting distribution of the averaged periodogram matrix, of memory estimates for nonstationary series, and for frequency domain regression estimates under nonstandard conditions.