MCEstimation function

A function to estimate the transition matrix for a discrete time Markov chain.

This function estimates the transition matrix for a discrete time Markov chain with state space 0,1,..,n given a realisation. The chain has n+1 states.

MCEstimation(statehist,n)

Arguments

• statehist: the realisation of the chain.
• n: the highest numbered state.

Details

We assume that the state space is 0,1,2...,n. n is assumed known as it cannot be reliably infered from the realisation.

Returns

Returns the empirical transition matrix obtained by calculating the observed frequencies of actual transitions in the realisation.\

References

Jones, O.D., R. Maillardet, and A.P. Robinson. 2009. An Introduction to Scientific Programming and Simulation, Using R. Chapman And Hall/CRC.

See Also

MCSimulation

Examples

P <- matrix(c(0.5,0.5,0,0,0.7,0.1,0.2,0,0,0.1,0.1,0.8,0,0,0.7,0.3),
            nrow = 4, ncol = 4, byrow = TRUE)
statehist<-MCSimulation(P, 0, 3000)
MCEstimation(statehist, 3)