I have multiple time series; all cumulative starting from 0 to 1, and the duration of all is equal to 1 (standardized). Is there a way to produce random time series using Monte Carlo simulation (probabilistic modeling)?

I'm trying to generate multiple random cumulative time series via Monte Carlo by using a limited number (e.g., three) of cumulative time series.
Let's say: y=f(t). We have the three following time series (y1y3), in which each element corresponds to one time on 't' vector:
t = [0,0.25,0.50,0.75,1]
y1 = [0,0.2,0.5,0.85,1]
y2 = [0,0.1,0.3,0.7,1]
y3 = [0,0.3,0.6,0.8,1]
Now want to generate 100 'y' whose begin with 0 and ends with 1, but their intermediate values can differ from y1y3. In other words, at each time (t), we have a stochastic element (e.g., y(t)) bounded by the min and max of y1(t), y2(t) and y3(t). The elements are not quite independent from the earlier time steps. For instance, y(t+1) must be greater or equal to y(t) (these are cumulative time series).
Let me know if my question's still not clear.
Thanks! 
So you want to do something like this?
1) at time = 0.25, sample a distribution with a min of 0.1 and and a max of 0.3
2) at time = 0.5, sample a distribution with a mind of 3 and a max of 0.6)
3) at time = 0.75, sample a distribution with a min of 0.6 and a max of 0.85What is the shape of the the distribution? Uniform, triangular?
Why do you think this is statistically defensible? 
Correct. That's exactly what I want. The PDF's subjective but most likely uniform.
Is it possible to be done in GoldSim? Can the elements of a time series be stochastic?
In a statistical modeling perspective, I'm trying to see how the uncertainty of time series shape of an input impacts the model output. 
The items in a Time Series cannot be Stochastic, but what you can do is create a Time Series with multiple series (e.g., 10, 100), and then tell GoldSim to randomly sample one each realization. Read here to see how to do this: https://www.goldsim.com/Help/#!Modules/5/definingmultipletimeseriesinasingletimeserieselement.htm

Somthing to messed up with the link. paste this directly into your browser:
https://www.goldsim.com/Help/#!Modules/5/definingmultipletimeseriesinasingletimeserieselement.htm
It is also in the GoldSim Help file under Time Series (defining multiple time series)
Please sign in to leave a comment.
Comments
12 comments