verifyMarkovProperty {markovchain}

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. In case a cell in the empirical transition matrix is >0 that is 0 in the theoretical transition matrix the null hypothesis is rejected.

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 results be 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. In case a cell in the empirical transition matrix is >0 that is 0 in the theoretical transition matrix the null hypothesis is rejected. In that case a p-value of 0 and statistic and dof of NA are returned.

a list of transition matrices?

Author(s)

Tae Seung Kang, Giorgio Alfredo Spedicato

References

Anderson and Goodman.

See Also

markovchain

Examples

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)