  We derive expressions for the predicitive information rate (PIR) for the
class of autoregressive Gaussian processes AR(N), both in terms of the
prediction coefficients and in terms of the power spectral density. The latter
result suggests a duality between the PIR and the multi-information rate for
processes with mutually inverse power spectra (i.e. with poles and zeros of the
transfer function exchanged). We investigate the behaviour of the PIR in
relation to the multi-information rate for some simple examples, which suggest,
somewhat counter-intuitively, that the PIR is maximised for very `smooth' AR
processes whose power spectra have multiple poles at zero frequency. We also
obtain results for moving average Gaussian processes which are consistent with
the duality conjectured earlier. One consequence of this is that the PIR is
unbounded for MA(N) processes.
