[pup55]

$this->bbcode_second_pass_quote('', 'h')ave the shocks shift the verhulst locally as well

[EnergySpin]

$this->bbcode_second_pass_quote('pup55', '')$this->bbcode_second_pass_quote('', 'h')ave the shocks shift the verhulst locally as well

[Shiraz]

$this->bbcode_second_pass_quote('', 'D')id you estimate URR with each local fit, or you kept that parameter fixed?

[khebab]

Another idea: if you look at the z-score of the residuals (green curve above) we can see clearly periodic fluctuations with about a 50 years period. So why not using the periodicity transform to extrapolate future shocks (see Price Prediction Based on the Periodicity Transform for details about the periodicity transform).

Here the methodology I followed:
1- in order to have a little more data in the future, I assume that the production will keep up with the population growth in order to keep a constant number of barrels per capita of about 4.5 (see thread Production Forecast with a Population Constraint for more details).
2- I fit the GBM parameters up to 2015 using URR= 2000 Gb
3- I compute the residuals in the log domain between the Bass Model (x(t)=1) which are then normalized to obtain the z-score (green curve below)
4- I apply the periodicity transform on the above z-score
5- I extend the resulting periodicity basis up to 2200 (red dashed curve below)
6- the extended z-score is then used as the control function x(t) for the GBM model

The different functions are shown below:



The two resulting GBM functions are shown below:



Using the original Guseo's shock function based on exponential shock we obtain a peak in 2017 with an URR of 1,854 Gb (black curve). This particular shock function tends toward infinity which means infinite investment to extract further oil past 2004!

The new shock function is based on an extrapolation of the observed cycles in the z-score function and is, I think, more realistic because it reaches a maximum value in 2017 which is just above the levels reached in the 70s. It suggest investments by the industry of the same order of magnitude in order to satisfy demand up to 2015. This effort collapses in 2017 producing a production peak around 2014. Interestingly, the resulting URR is smaller and is around 1,556 Gb which is near the ASPO estimate!

[khebab]

$this->bbcode_second_pass_quote('Shiraz', 'T')o try to bring this back to reality, you can see what I'm getting at in Khebabs GBM chart (above). Look at the 'control model' (purple). It is an approximation of 'Z score of the GBM without shocks' (green). Notice the fit is quite nice inside the fitting domain (ie yr < 2005). But what happens outside this domain? Well we KNOW the trend in the Z score is zero. After all, they are z scores. By comparison the control model appears to rise exponentially. In my experience, this is almost always the case with GBM models. That is also the conclusion I was getting at in the previous paragraph - that ouside the fitting domain, the tension between exponential curves would resolve to an exponential difference between the original trend and the continuation of the fitted curve. The problem with the GBM for me is that the control function always exhibits this 'aberant' behaviour outside the fitting domain.

[khebab]

To add to the discussion, I added the inflation adjusted crude oil price along to the different z-score curves:



Before the 80s, price spikes are correlated with negative shocks due to disruptions in production and runaway demand. In the 80s-90s, we lived from the oil glut created from the previous initial positive shocks. Prices and investments collapsed till the end of the 90s. Now it's different, prices are going up due to excessive demand and are calling for a new wave of investment in oil extraction and exploration that will probably peak before 2020. This new injection of capital will be probably enough to delay the PO date until 2014 (best case scenario) before global production will be overwhelmed by depletion.