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  • $\begingroup$ Hypothetically, in case I have an AR(3) mean model, which can be estimated as simple OLS, but with long memory errors, can I, according to your suggestion, just run the OLS for the mean and then use ARFIMA model for the residuals and use the fitted values as weights for Weighted least squares? $\endgroup$ Commented Mar 27, 2015 at 11:29
  • $\begingroup$ Could you be more explicit? Do you want to (1) model your dependent variable as AR(3) and then (2) model the residuals as ARFIMA($p,d,q$)? That does not make sense to me. Later, I did not understand what fitted values you would use, and what model you would estimate using WLS. $\endgroup$ Commented Mar 27, 2015 at 11:32
  • $\begingroup$ Well my first choice was ARIMA FIGARCH model, but it can't be done in R, therefore I thought I could found the conditional variances(to weight the original data points as you have written) using the ARFIMA on the squared residuals, which as I understand from the literature is as if I run the Figarch and consequently there wouldn't be heteroscedascity in the WLS $\endgroup$ Commented Mar 27, 2015 at 12:40
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    $\begingroup$ No, ARFIMA on squared residuals is not FIGARCH -- just as ARIMA on squared residuals is not GARCH. AR(F)IMA model has an error term so that the modeled relationship is approximate. Meanwhile, (F)IGARCH is deterministic in the sense that there is no error in the (F)IGARCH formula. That is, the conditional variance is supposedly perfectly explained in the (F)IGARCH model. AR(F)IMA on squared residuals is more like a stochastic volatility model (note the name stochastic as opposed to deterministic, which is true for (F)IGARCH). $\endgroup$ Commented Mar 27, 2015 at 12:52
  • $\begingroup$ All right, I see it now and it brings me back where I started, but thank you for your explanation $\endgroup$ Commented Mar 27, 2015 at 13:08