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Number of MC Simulations in Multivariate Model with Copulas

Cross Validated Asked on November 6, 2021

I am working on a project with the following characteristics:

  • 4,000 hydroelectricity generation time series
  • 800 futures time series (each corresponding to at least one hydroelectricity time series)
  • Each of the above is fitted to its own statistical distribution (resulting in 4,800 processes)
  • t-distribution copulas describe the generation series (based on Pearson correlation)
  • t-distribution copulas describe the futures series (based on Spearman correlation)

The goal is to obtain the 5th percentile of the expected revenue in such a system via Monte Carlo simulation, such that revenue is the sum of revenues at each hydroelectricity generation, where revenue at each system is the product of hydroelectric generation and the price of the respective futures.

My question is: how many simulations are enough, given the copula structure and the number of variables in play? The resources I’ve encountered on the web address cases far simpler than mine, and even their estimates vary wildly, so I was hoping your kind expertise could help.

Thank you!

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