Simulate from a higher order multivariate Markov chain

Simulates the next t states of each sequence of a higher order multivariate Markov chain, given their last order states.

Usage

predictHommc(hommc, t, init)

Arguments

hommc: An hommc object, for instance fitted by fitHighOrderMultivarMC().
t: Number of steps to simulate, a positive integer.
init: A matrix with one row per sequence and order columns, the last states of each sequence, the most recent in the last column. If missing, every sequence starts from the first state, repeated.

Value

A character matrix with one row per sequence and t columns, the simulated states.

Details

At each step the next state of sequence \(j\) is drawn from \(\sum_k \sum_h \lambda_{jkh} P_h^{(jk)} x^{(k)}_{t-h+1}\), where \(x^{(k)}_{t-h+1}\) is the state of sequence \(k\) \(h - 1\) steps before the current one (Ching et al., 2008). The matrices are read by column (P[to, from]), as returned by fitHighOrderMultivarMC(), or by row when the byrow slot of hommc is TRUE; all the sequences are drawn from the same past before it is updated.

References

Ching, W.-K., Ng, M. K. and Fung, E. S. (2008). Higher-order multivariate Markov chains and their applications. Linear Algebra and its Applications 428(2-3), 492-507. doi:10.1016/j.laa.2007.05.021

Author

Vandit Jain

Examples

data <- matrix(c("2", "1", "3", "3", "4", "3", "2", "1", "3", "3", "2", "1",
                 "2", "4", "4", "4", "4", "2", "3", "3", "1", "4", "3", "3"),
               ncol = 2)
if (requireNamespace("Rsolnp", quietly = TRUE)) {
  fit <- fitHighOrderMultivarMC(data, order = 2, Norm = 2)
  # the last two states of each sequence
  init <- t(data[11:12, ])
  predictHommc(fit, 5, init)
}
#> This function is experimental
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,] "1"  "3"  "3"  "4"  "2" 
#> [2,] "1"  "4"  "4"  "2"  "3"