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Test the first-order Markov property of an empirical sequence

Source: R/statisticalTests.R
statisticalTests.Rd

Tests the null hypothesis that the conditional distribution of the next state depends only on the current state, against a second-order alternative.

Tests whether the sequence is compatible with a first-order Markov chain against a second-order alternative, by testing independence of past and future states conditional on the present state. Degrees of freedom are summed, present-state by present-state, over only the past and future states actually observed with that present state, mirroring the other functions documented on this page.

Tests whether transition probabilities are constant across consecutive blocks. Structural zeros can be supplied explicitly through a logical transition matrix.

Usage

verifyMarkovProperty(
  sequence,
  method = c("G", "Pearson", "simulation"),
  B = 9999,
  seed = NULL,
  verbose = TRUE
)

assessOrder(sequence, verbose = TRUE)

verifyEmpiricalToTheoretical(
  data,
  object,
  method = c("G", "Pearson", "simulation"),
  B = 9999,
  seed = NULL,
  verbose = TRUE
)

verifyHomogeneity(
  inputList,
  method = c("G", "Pearson", "simulation"),
  B = 9999,
  seed = NULL,
  verbose = TRUE
)

assessStationarity(sequence, nblocks, structural.zeros = NULL, verbose = TRUE)

Arguments

sequence

An empirical sequence.

method

Test statistic: `"G"`, `"Pearson"`, or `"simulation"`.

B

Number of Monte Carlo replicates for simulation.

seed

Optional random seed.

verbose

Should test results be printed?

data

An empirical sequence or a matrix of transition counts.

object

A `markovchain` object specifying theoretical probabilities.

inputList

A list whose elements are empirical sequences or matrices.

nblocks

Number of blocks, at least two.

structural.zeros

Optional logical matrix marking impossible transitions.

Value

An `htest` object with additional package-specific components.

An `htest` object.

An `htest` object with observed and expected counts.

An `htest` object with pooled and individual transition counts.

An `htest` object.

References

Anderson, T. W. and Goodman, L. A. (1957). Statistical inference about Markov chains. *The Annals of Mathematical Statistics*, 28(1), 89–110.

Kullback, S., Kupperman, M. and Ku, H. H. (1962). Tests for Contingency Tables and Markov Chains. *Technometrics*, 4(4), 573–608.

Anderson, T. W. and Goodman, L. A. (1957). Statistical inference about Markov chains. *The Annals of Mathematical Statistics*, 28(1), 89–110.