Markov Processes: Estimating Transition Probabilities

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SUMMARY

This discussion focuses on estimating transition probabilities for Markov matrices, emphasizing the application of Maximum Likelihood Estimation (MLE) on sample data. Participants highlight the importance of calculating sample proportions, specifically the frequency of transitions between states divided by the total number of transitions. The conversation also touches on the inclusion of self-transitions (j=i) in the calculations and queries about the use of mixture models in conjunction with Black-Scholes theory.

PREREQUISITES
  • Understanding of Markov processes and transition matrices
  • Familiarity with Maximum Likelihood Estimation (MLE)
  • Knowledge of discrete and continuous probability distributions
  • Basic concepts of mixture models and their applications
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  • Research the implementation of Maximum Likelihood Estimation for Markov models
  • Explore sample proportion calculations in Markov processes
  • Investigate the application of mixture models in financial contexts, particularly with Black-Scholes
  • Study the differences between discrete and continuous Markov processes
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Researchers, data scientists, and statisticians interested in Markov processes, transition probability estimation, and applications in financial modeling.

WWGD
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Hi,
What are recent results on estimating transition probabilities for Markov matrices. I believe @BvU works in that general area?
 
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Sorry, but: no !
 
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WWGD said:
Hi,
What are recent results on estimating transition probabilities for Markov matrices.
Based on what? Do you have sample data of single-step transitions?
 
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Are there several options? Im not aware on what area /aspect to sample.I think , yes, iirc, they applied MLE to sample data, but I couldn't come up with the actual statistic .
 
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FactChecker said:
Based on what? Do you have sample data of single-step transitions?
Edit: Sample proportions; number of times there has been a transition between states i and j, divided by total number of transitions/states ( for the discrete case)s, or anything else that's available for the continuous case .
 
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WWGD said:
Edit: Sample proportions; number of times there has been a transition between states i and j, divided by total number of transitions/states ( for the discrete case)s, or anything else that's available for the continuous case .
I would divide by the number of samples that were in state i before the single step. Also, j=i should be included.
 
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Do you know of mixture models that use Black Sholes?
 

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