Some problems in the overspeci cation of ARMA and ARIMA processes using ARFIMA models

Nonstationary ARIMA processes and nearly nonstationary ARMA processes, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in practice, almost indistinguishable from those of a stationary longmemory process, such as a Fractionally Integrated ARMA (ARFIMA) process. Because of this, model misspeci cation may occur in trying to distinguish between the di erent processes. An appealing strategy would be to overspecify the model and estimate the integration parameter. In this paper, we investigate the e ects of this type of misspeci cation on parameter estimates using either spectral regression or frequency-domain maximum likelihood methods.