Generating Random Time Series from Multiple Deterministic Time Series

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    Rick Kossik

    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

    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.

  • Avatar
    Rick Kossik

    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

    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!

  • Avatar
    Rick Kossik

    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

    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.

  • Avatar
    Rick Kossik

    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

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

  • Avatar
    Rick Kossik

    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

    It works. Thanks!

  • Avatar
    Ebrahim Ahmadisharaf

    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

    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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