hdMTD (version 0.1.4)

hdMTD_CUT: The CUT method for inference in MTD models

Description

A function that estimates the set of relevant lags of an MTD model using the CUT method.

Usage

hdMTD_CUT(
  X,
  d,
  S = seq_len(d),
  alpha = 0.05,
  mu = 1,
  xi = 0.5,
  A = NULL,
  warn = FALSE,
  ...
)

Value

Returns a set of relevant lags estimated using the CUT algorithm.

Arguments

X

A vector or single-column data frame containing a chain sample (X[1] is the most recent).

d

A positive integer representing an upper bound for the chain order.

S

A numeric vector of distinct positive integers from which this function will select a set of relevant lags. Should be a subset of 1:d. Default is 1:d.

alpha

A positive real number used in the CUT threshold (which determines if two distributions can be considered different). The larger the alpha, the greater the distance required to consider that there is a difference between a set of distributions.

mu

A positive real number such that \(\code{mu}>(e^{\code{mu}}-1)/2\). mu is also a component of the same threshold as alpha.

xi

A positive real number, xi is also a component of the same threshold as alpha.

A

A vector with positive integers representing the state space. If not informed, this function will set A <- sort(unique(X)).

warn

Logical. If TRUE, the function warns the user when A is set automatically.

...

Additional arguments (not used in this function, but maintained for compatibility with hdMTD().

Details

The "Forward Stepwise and Cut" (FSC) is an algorithm for inference in Mixture Transition Distribution (MTD) models. It consists in the application of the "Forward Stepwise" (FS) step followed by the CUT algorithm. This method and its steps where developed by Ost and Takahashi and are specially useful for inference in high-order MTD Markov chains. This specific function will only apply the CUT step of the algorithm and return an estimated relevant lag set.

References

Ost, G. & Takahashi, D. Y. (2023). Sparse Markov models for high-dimensional inference. Journal of Machine Learning Research, 24(279), 1-54. http://jmlr.org/papers/v24/22-0266.html

Examples

# Simulate a chain from an MTD model
set.seed(1)
M <- MTDmodel(Lambda = c(1, 4), A = c(1, 3), lam0 = 0.05)
X <- perfectSample(M, N = 400)

# Apply CUT with custom alpha, mu, and xi
hdMTD_CUT(X, d = 4, alpha = 0.02, mu = 1, xi = 0.4)

# Apply CUT with selected lags and smaller alpha
hdMTD_CUT(X, d = 6, S = c(1, 4, 6), alpha = 0.08)