Markov Processes: Estimating Transition Probabilities

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Discussion Overview

The discussion centers on estimating transition probabilities for Markov matrices, exploring recent results and methodologies. Participants inquire about sampling techniques and statistical approaches relevant to this topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks about recent results in estimating transition probabilities for Markov matrices and references another participant's expertise.
  • Another participant expresses uncertainty about their involvement in the topic.
  • A participant requests clarification on the basis for estimating transition probabilities and inquires about sample data for single-step transitions.
  • There is a suggestion that maximum likelihood estimation (MLE) may be applicable, though the participant is unsure of the specific statistics involved.
  • A participant elaborates on the concept of sample proportions, detailing how to calculate transitions between states in both discrete and continuous cases.
  • Further clarification is provided on the calculation method, emphasizing the importance of including transitions where the state remains the same.
  • A participant introduces a question regarding the use of mixture models in relation to Black-Scholes, indicating a potential connection to the topic.

Areas of Agreement / Disagreement

Participants express varying levels of knowledge and uncertainty regarding the methodologies for estimating transition probabilities, indicating that multiple competing views and approaches remain unresolved.

Contextual Notes

Limitations include a lack of consensus on specific statistical methods and the need for sample data to support claims about transition probabilities.

Who May Find This Useful

Researchers and practitioners interested in Markov processes, statistical estimation methods, and applications in finance may find this discussion relevant.

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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