Generating Random Time Series from Multiple Deterministic Time Series

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Ebrahim Ahmadisharaf

• October 30, 2017 14:02

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)?

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  Rick Kossik

  • October 30, 2017 18:13

  I don't understand what you mean that the duration of all is equal to 1.  A time series is , by definition, a list of either dates/times or elapsed times.

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  Ebrahim Ahmadisharaf

  • October 30, 2017 18:23

  example time in the time series: [0,0.25,0.5,0.75,1].
  
  and a little more on my problem: this is a cumulative rainfall distribution such as SCS. I have a bunch of them here and want to generate random time series out of them.

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  Rick Kossik

  • October 30, 2017 18:28

  I still don't understand. You want to produce random time series.  But based on what?  What is the input data?  How do you want to sample?  You must be more specific.

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  Ebrahim Ahmadisharaf

  • October 30, 2017 18:44

  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 (y1-y3), 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 y1-y3. 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!

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  Rick Kossik

  • October 30, 2017 18:58

  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 0.85

  What is the shape of the the distribution? Uniform, triangular?
  Why do you think this is statistically defensible?

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  Ebrahim Ahmadisharaf

  • October 30, 2017 19:05

  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.

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  Rick Kossik

  • October 30, 2017 19:37

  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 

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  Ebrahim Ahmadisharaf

  • October 30, 2017 19:39

  thanks! I can't open the link though ('the page cannot be found'). any alternate source?

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  Rick Kossik

  • October 30, 2017 19:43

  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)

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  Ebrahim Ahmadisharaf

  • November 01, 2017 01:27

  It works. Thanks!

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  Ebrahim Ahmadisharaf

  • January 31, 2018 00:22

  Is it possible to assign a probability to each time series, so that each time series has a unique probability? For example, if we have three time series, can we assign the unique probability of 0.2, 0.4 and 0.2 to the three time series, respectively?

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  Rick Kossik

  • February 05, 2018 16:29

  Define a Discrete Distribution with three values (0.2, 0.4. 0.2).  Enter this as the Active Realization for the Time Series.

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