Is it really that important?

We are talking an approximation here.

Let's assume the real world shocks are roughly evenly spread out in time, then the noise stays there, but does not affect the overall conclusion that much.

Also, whether the shocks have a relative big enough scale to matter, remains to me at least unproven.

I think the model has a lot of potential and cleaning the real world data would also have it's consequences, just as WHT points out. There have already been other methods using various ways of trying to average out the noise, perhaps introducing additional skew to the data for future extrapolation.

Modelling it with noise intact at least starts with a different premise and the results are encouraging.

However, in an ideal scenario, I think your point about trying to achieve 'perfect world' scenario is a good one.

BTW, great work WHT. Even a person like me who's getting back to physics/maths after at 15+ hiatus could follow the main gist of the article much of the time. That is quite remarkable communication and explanation powers you have!

Well, if you take the global oil production curve and work out the offsets, translations and stretching necessary to turn that shape into a smooth bell curve unconstrained consumption theory predicts - you can readily see how the effects I describe can have a key impact on production data. Its not a big step to suggest the effect is equivalent or greater in other areas.

So yes, I'd say its important.

Your points may have validity which might be checked by doing a sensitivity analysis, but one needs to start with a model, and the simplier the better. With a model in hand, one can introduce factors as you mention, and see how the model results deviate from the data. You can't reject the model as insignificant when you don't know how it responds to the input you suggest.

My suggestion is rather the reverse.

Take out of the base data the effect of known factors, then model the now simpler data. No mathematical equation will match the discontinuous actions of politics and economics - but take them out and you have a chance.

Once you have the model, add the effects back in.

I understand your point. The step changes I think are very deterministic and happen at the last stage of the process, which is why I call them shocks. Everything else about the model is stochastic (one could argue about the power-law growth term, but everything has to have a driving force). So if I could divine what the extractive step changes are, preferably from some real world source, like corporate records or OPEC dictates, I certainly would be more satisfied. Apart from that, having a reasonable set of dimensional parameters that derive from some simple physical models helps to fill in the rest of the puzzle.