Difference between revisions of "How to Estimate a Transition Matrix"
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How to Estimate a Transition Matrix
This entry is an overview of the steps required to estimate a Transition Matrix. The outcome of such an exercise is an Empirical Transition Matrix (estimated from observed data).
- In general a transition matrix will be just one quantitative element in broader toolkit of risk models
- There is no particular assumption of the domain / context of the exercise so the steps are quite general.
- Depending on the business and the regulatory context / importance of the calculation there might be more specific formal requirements (e.g. with respect to adequacy of data, data cleaning procedures etc)
- In many specific situations some steps might not be needed or others might be required.
Activities can be grouped in four broad stages.
The Four Stages of a Transition Matrix Lifecycle
Stage 1: Preliminary Considerations
This stage defines the scope and objectives and overall shape of the transition matrix development.
- Identifying the relevant State Space from prior business knowledge or by inspecting the data
- Preliminary Data Collection, Data Cleansing, Exploratory Data Analysis of the data that we will use
Stage 2: Transition Matrix Estimation
This stage captures the main statistical work. There is a variety of estimation methods with trade-offs in simplicity / accuracy:
These methods are estimating empirical transitions. The more general estimation problem in the context of more elaborate model development may involve static or dynamic covariates.
Stage 3: Transition Matrix Validation
The model validation stage (sometimes bundled or iterated with the previous development stage) provides a more or less formal review of the development stage.
- Statistical significance, especially when transition rates are low
- Reasonableness of transition probabilities / concurence with prior knowledge / expectations
- Validity of estimation assumptions (e.g. time homogeneity, markov nature etc.)
Stage 4: Using Transition Matrices
Depending on the context this stage includes Production Implementation, Acceptance Testing, User Training and ongoing use of the developed estimates. A transition matrix might be used in various ways:
- As-is (Inspecting the values)
- Embedded in an analytic calculation / model
- As input to a simulation model
In contexts where there is ongoing collection of new (or additional) data there may be a need to periodically update the estimates
Open Source Implementations
- https://github.com/open-risk/transitionMatrix
- Analysis of Credit Migration using Python TransitionMatrix