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. The more critical the use of the outcomes the more likely that this phase must conform to formal requirements around Model Development, including explicit specifications about Data Quality etc. Indicative steps in this stage might include:

Preliminary Data Collection from one or more IT systems, databases etc.
Data Cleansing
Exploratory Data Analysis

Outcomes of this phase will be among others:

Identifying the relevant State Space by integrating prior business knowledge and/or by inspecting the data

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:

The Cohort Estimator
The Aalen-Johansen Estimator

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

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How to Estimate a Transition Matrix

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