Markov Chains analysis and rendering tools

Fabio Caironi, Università degli Studi di Milano

Introducion

This package is endowed with several tools for analyzing discrete homogeneous Markov chains. Namely: a graph rendering section, an analysis summary section and a simulation section. MC's here are treated as object of the class markovchain, which is defined in the omonimous package markovchain. In fact, this package leans on the latter as for MC's implementation and analysis, nonetheless provides a user-friendly rendering through a shiny app.

Shiny app

Run the mctools shiny app and start working.

library(mctools)
GUI()

Here below the MC's acquisition methods and outputs are listed and described.

Manual input

A page dedicated to keyboard input will open as soon as the shiny app is run. Here you can create a Markov Chain by specifying the number of states, the names of the states and the transition matrix. All data you enter will be properly validated before creating any Markov Chain.

Dataset input

The data input sidebar allows you to load data exported from the official ESMA Central Repository, concerning rating activity and rating performance of Credit Rating Agencies (CRA). These statistics are available over a user-chosen period and rating type, for each CRA. You should also specify a time horizon (Short term / Long term). In our context, what is interesting are the Transition matrices of the rating activity, that you can download as a .csv file using the dedicated icon at the top right of the page. The specific format of those files is a requirement for retrieving correctly the transition matrix, so do not try to read from a differently structured file. Five sample files downloaded from ESMA are available in the package as well (and are presented in a selection list in the shiny app).

Graph

A graph is rendered through the diagram package. Please, note that mctools is intended for small-dimensioned discrete Markov chains: although analysis and simulation will display outputs quite tidily even for a great number of states, the diagram plot won't look nice in that case (for rendering graphs with many nodes, such as social networks graphs, check out here).

Summary

In this section you can find a complete analysis of your MC. This will include analysis of reducibility, regularity, periodicity of MC, classification of its states, existence of stationary distributions and probabilistic analysis.

Simulation

Thanks to a built-in function for MC's simulation provided by markovchain, this section allows you to simulate your MC by picking and initial state and a sample dimension.

Functions

The package contains several functions for data acquisition, parsing and text printing. You can check their usage in the documentation:

? percToNum
? matrixBuilder
? mat_val
? mat_gen
? ESMAtransRateReader
? printRows
? printVecNames

External references

To have an in-depth review of the package markovchain and its applications you may find very useful its vignette An introduction to markovchain package.

Authors

Fabio Caironi - MCs student of Data Science and Economics @ Unimi. Github: https://github.com/fabio130497

fabcairo/mctools