multi.mtd {GenMarkov}

Estimation of Multivariate Markov Chains - MTD model

Description

This function estimates the Mixture Distribution Model (Raftery (1985)) for Multivariate Markov Chains. It considers Berchtold (2001) optimization algorithm for the parameters and estimates the probabilities transition matrices as proposed in Ching (2002).

Usage

multi.mtd(y, deltaStop = 1e-04, is_constrained = TRUE, delta = 0.1)

Arguments

y

matrix of categorical data sequences

deltaStop

value below which the optimization phases of the parameters stop

is_constrained

flag indicating whether the function will consider the usual set of constraints (usual set: TRUE, new set of constraints: FALSE).

delta

the amount of change to increase/decrease in the parameters for each iteration of the optimization algorithm.

Value

The function returns a list with the parameter estimates, standard-errors, z-statistics, p-values and the value of the log-likelihood function, for each equation.

Note

See details of the optimization procedure in Berchtold (2001).

References

Raftery, A. E. (1985). A Model for High-Order Markov Chains. Journal of the Royal Statistical Society. Series B (Methodological), 47(3), 528-539. http://www.jstor.org/stable/2345788

Berchtold, A. (2001). Estimation in the Mixture Transition Distribution Model. Journal of Time Series Analysis, 22(4), 379-397.doi:10.1111/1467-9892.00231

Ching, W. K., E. S. Fung, and M. K. Ng (2002). A multivariate Markov chain model for categorical data sequences and its applications in demand predictions. IMA Journal of Management Mathematics, 13(3), 187-199. doi:10.1093/imaman/13.3.187

Examples

data(stockreturns)
s <- cbind(stockreturns$sp500, stockreturns$djia)
multi.mtd(s)