higherOrderPredict: Next-state probabilities and simulation for higher order...

In markovchain: Easy Handling Discrete Time Markov Chains

Next-state probabilities and simulation for higher order Markov chains

Description

higherOrderPredict returns the distribution of the next state given the most recent states, and higherOrderSimulate draws a sequence of states, under a higher order model fitted by fitHigherOrder or fitMTD.

Usage

higherOrderPredict(fit, history)

higherOrderSimulate(n, fit, t0, include.t0 = FALSE)

Arguments

fit	The list returned by fitHigherOrder or fitMTD.
history	The most recent states, oldest first: a vector of at least order states, or a matrix (or data frame) with one history per row.
n	Number of states to simulate.
t0	The states preceding the simulated ones, oldest first; at least order states.
include.t0	Should t0 be included at the beginning of the returned sequence?

Details

Both functions use the transition probabilities of the fitted model of order k,

P(x_t = j \mid x_{t-1}, \dots, x_{t-k}) = \sum_{i=1}^{k} \lambda_i\, Q_i[j, x_{t-i}],

the same that enter higherOrderLogLik. For a fit returned by fitMTD all the Q_i are the single MTD transition matrix. Only the last k states of a history are used, the last element being the most recent.

A model of order k needs k previous states, so t0 (and every history) must contain at least order states. The probabilities are normalized to sum to one, which only matters when the weights of a least squares fit sum to one up to the optimizer's tolerance.

Value

higherOrderPredict: a named vector of next-state probabilities for a single history, or a matrix with one row per history. higherOrderSimulate: a character vector of n states, preceded by t0 if include.t0 = TRUE.

See Also

fitHigherOrder, fitMTD, higherOrderLogLik, rmarkovchain

Examples

wind <- read.csv(system.file("extdata", "koeberg_wind.csv",
                             package = "markovchain"))$state
fit <- fitMTD(wind, order = 2)
# next wind direction after directions 1 and then 2
higherOrderPredict(fit, c(1, 2))
# several histories at once
higherOrderPredict(fit, rbind(c(1, 1), c(2, 2), c(4, 1)))
# simulate one day of hourly directions starting from the last two observed
set.seed(1)
higherOrderSimulate(24, fit, t0 = tail(wind, 2))

# the same works for fitHigherOrder()
data(rain)
fit2 <- fitHigherOrder(rain$rain, order = 2, method = "mle")
higherOrderPredict(fit2, c("0", "6+"))

markovchain documentation built on Oct. 10, 2026, 9:07 a.m.