I would like to compare the variability of two model runs with a random input (a base price + noise). I am interested in seeing how different "policies" will control or fail to control variability in other model components. This is related to my work on payments for environmental services.
I can run a sensitivity analysis with my noise seed set as random uniform with step of 1. Then I can see how different "policies" can limit or control variation in the face of varying prices.... using graphical output and the stats tool.
I am aware that I should to cut off the first part of the output (by adjusting on the time axis tool) for the stat analysis since it takes time for the model to develop full variability. Is there any special way to decide when the model has reached this point?
In the back of my mind I have the vague notion that looking at this output over time is not the way to do this..... (I will have to look at my advanced course notes ).
I am not sure I really understand the question, but I guess my reply may not make much sense either.
As far as getting to steady state - if the system is ergodic this occurs at the time when the distribution of values across simulations becomes invariant or, equivalently, the distirbution from that the chosen time forward is the same as the distirbution from a later chosen time forward. The easiest way to visualize this is to use the Sensitivty Graph and pick a time after the percentile lines all become constant. If the percentile lines do not become constants the system is not ergodic.
If the system is ergodic - which you seem to be assuming - it does not matter if you look at variation over time or variation across simulations. If it is not, everything is much murkier and there is no real clear way to proceed beyond using common sense.
When varying noise seed use a large range - ie 0 to 1e9.
What I was trying to do is get a general measure of variability in selected model components. How much do these jump around when price has a random component. My "goal" is to keep these components relatively stable in spite of the added noise. I was hoping ot have an easy measure of this "jumping around" and want to see which policies will make things stabalize in spite of the noise.
Ergodic means that if you look at behavior from time 3000-4000 or from 22000-23000 there is no discernble difference. It is a random steady state concept.
For your example do as I said - put in randomness in the run, then do Sensitivity on NOISE SEED (0 to 1e9) for 1,000 replications. find the time where the sensitivity graphs plots stop changing. A little past that is the start time for testing variability.
No go back to single simulations and just run different policies. You should be sure you have at least 1,000 time steps after your measurement start to get decent confidence (sometimes as many as 1,000,000 are required).
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