the AR model replicates the observed first- order (variance) and second order (correlation) residual statistics:
Then, for each production maturity levels (20% to 80%) , I generate 1,000 random realizations of the residuals which I add to the "true logistic model" before using the Hubbert linearization to estimate the URR and K.
Results
The distribution of the sample estimates for the URR and K at 50% of maturity are the following:
Distribution of the 1,000 samples' estimates at 50% of maturity. The full red line is the median value and the two dotted red lines are the limits of the 80% confidence interval.
Discussion
1- K estimation is more reliable than the URR
2- if we are near 50% of maturity (peak production) the uncertainty on the URR estimation is quite large and the 90% confidence interval is [1.551, 3.854] Tb with a median estimate around 2.335 Tb which covers the ASPO and USGS lower estimates.
3- Assuming a given URR we have about 30% chance to be wrong by more than 10% (higher or lower) if we are near peak production.
4- The Hubbert linearization seems to be fairly reliable even if residuals are strongly correlated
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