| Abstract: | Abstract. We look at the implications of modeling observations from a fractionally differenced noise process using an approximating AR ( p ) model. The approximation is used because of computational difficulties in the estimation of the differencing parameter of the fractional noise model. Because the fractional noise process is long-range dependent, we assess the applicability of the approximating autoregressive (AR) model based on its long-range forecasting accuracy compared with that of the fractional noise model. We derive the asymptotic k -step-ahead prediction error for a fractional noise process modeled as an AR( p ) process and compare it with the k -step-ahead prediction error obtained when the model for the observed series is correctly specified as a fractional noise process and the fractional differencing parameter d is either known or estimated. We also assess the validity of the asymptotic results for a finite sample size via simulation. We see that AR models can be useful for long-range forecasting of long-memory data, provided that consideration is given to the forecast horizon when choosing an approximating model. |
