Large differences in ARFIMA parameter $d$ using different estimators

Question

I am trying to estimate parameter $d$ for ARFIMA model using different methods: Hurst, ML, fdSperio, fdGPH and the function arfima which selects the best fit automatically. The results shown are too large in difference, and I wonder why.

I attached an image of my coding:

Especially parameter $d$ from arfima, the value is too extreme. Other values are having big differences as well.

Also, this is brief explanation on what I am doing:

1. I am fitting ARFIMA model with my data: monthly Brent Oil Price.
2. Before that, I will need to estimate the values of $d$, and I am doing that with different methods as mentioned above.
3. After the values of $d$ are obtained, I will use diffseries to difference the series manually.
4. Then I will fit those differenced series into ARIMA model to compare their AICs, to find the best model.

Am I going to the right way? Please correct me if I am wrong.