  A moment bound for the normalized conditional-sum-of-squares (CSS) estimate
of a general autoregressive fractionally integrated moving average (ARFIMA)
model with an arbitrary unknown memory parameter is derived in this paper. To
achieve this goal, a uniform moment bound for the inverse of the normalized
objective function is established. An important application of these results is
to establish asymptotic expressions for the one-step and multi-step mean
squared prediction errors (MSPE) of the CSS predictor. These asymptotic
expressions not only explicitly demonstrate how the multi-step MSPE of the CSS
predictor manifests with the model complexity and the dependent structure, but
also offer means to compare the performance of the CSS predictor with the least
squares (LS) predictor for integrated autoregressive models. It turns out that
the CSS predictor can gain substantial advantage over the LS predictor when the
integration order is high. Numerical findings are also conducted to illustrate
the theoretical results.
