verifyMarkovProperty: Various functions to perform statistical inference of DTMC

Description

These functions verify the Markov property, assess the order and stationarity of the Markov chain.

This function tests whether an empirical transition matrix is statistically compatible with a theoretical one. It is a chi-square based test

Verifies that the s elements in the input list belongs to the same DTMC

Usage

verifyMarkovProperty(sequence, verbose = TRUE)
assessOrder(sequence, verbose = TRUE)
assessStationarity(sequence, nblocks, verbose = TRUE)
verifyEmpiricalToTheoretical(data, object, verbose = TRUE)
verifyHomogeneity(inputList, verbose = TRUE)

Arguments

sequence

An empirical sequence.

verbose

Should test resuls been printed out?

nblocks

Number of blocks.

data

matrix, character or list to be converted in a raw transition matrix

object

a markovchain object

inputList

A list of items that can coerced to transition matrices

Value

Verification result

a list with following slots: statistic (the chi - square statistic), dof (degrees of freedom), and corresponding p-value

a list of transition matrices?

References

Anderson and Goodman.

Examples

Run this code

sequence <- c("a", "b", "a", "a", "a", "a", "b", "a", "b",
              "a", "b", "a", "a", "b", "b", "b", "a")
mcFit <- markovchainFit(data = sequence, byrow = FALSE)
verifyMarkovProperty(sequence)
assessOrder(sequence)
assessStationarity(sequence, 1)


#Example taken from Kullback Kupperman Tests for Contingency Tables and Markov Chains

sequence<-c(0,1,2,2,1,0,0,0,0,0,0,1,2,2,2,1,0,0,1,0,0,0,0,0,0,1,1,
2,0,0,2,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,2,1,0,
0,2,1,0,0,0,0,0,0,1,1,1,2,2,0,0,2,1,1,1,1,2,1,1,1,1,1,1,1,1,1,0,2,
0,1,1,0,0,0,1,2,2,0,0,0,0,0,0,2,2,2,1,1,1,1,0,1,1,1,1,0,0,2,1,1,
0,0,0,0,0,2,2,1,1,1,1,1,2,1,2,0,0,0,1,2,2,2,0,0,0,1,1)

mc=matrix(c(5/8,1/4,1/8,1/4,1/2,1/4,1/4,3/8,3/8),byrow=TRUE, nrow=3)
rownames(mc)<-colnames(mc)<-0:2; theoreticalMc<-as(mc, "markovchain")

verifyEmpiricalToTheoretical(data=sequence,object=theoreticalMc)


data(kullback)
verifyHomogeneity(inputList=kullback,verbose=TRUE)