  This work aims at estimating inverse autocovariance matrices of long memory
processes admitting a linear representation. A modified Cholesky decomposition
is used in conjunction with an increasing order autoregressive model to achieve
this goal. The spectral norm consistency of the proposed estimate is
established. We then extend this result to linear regression models with
long-memory time series errors. In particular, we show that when the objective
is to consistently estimate the inverse autocovariance matrix of the error
process, the same approach still works well if the estimated (by least squares)
errors are used in place of the unobservable ones. Applications of this result
to estimating unknown parameters in the aforementioned regression model are
also given. Finally, a simulation study is performed to illustrate our
theoretical findings.
