mmcx {GenMarkov}

Non-homogeneous Multivariate Markov Chains

Description

Estimates Multivariate Markov Chains that depend on a exogeneous variables. The model is based on the Mixture Transition Distribution model, and considers non-homogeneous Markov Chains, instead of homogeneous Markov Chains as in Raftery (1985).

Usage

mmcx(y, x, initial, ...)

Arguments

y

matrix of categorical data sequences

x

matrix of covariates

initial

numerical vector of initial values.

...

additional arguments to be passed down to auglag().

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.

Author(s)

Carolina Vasconcelos and Bruno Damásio

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

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

See Also

Optimization is done through auglag().

Examples

data(stockreturns)
s <- cbind(stockreturns$sp500, stockreturns$djia)
x <- stockreturns$spread_1
mmcx(s, x, initial = c(1, 1))