hdMTD (version 0.1.4)

hdMTD_FSC: Forward Stepwise and Cut method for inference in MTD models

Description

A function for inference in MTD Markov chains with FSC method. This function estimates the relevant lag set \(\Lambda\) of an MTD model through the FSC algorithm.

Usage

hdMTD_FSC(X, d, l, alpha = 0.05, mu = 1, xi = 0.5, A = NULL, ...)

Value

Returns a vector with the estimated relevant lag set using FSC 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.

l

A positive integer that sets the number of elements in the output vector.

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. Defaulted to 0.05.

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)).

...

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.

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, 3), A = c(1, 2), lam0 = 0.05)
X <- perfectSample(M, N = 400)

# Forward Stepwise and Cut with different parameters
hdMTD_FSC(X, d = 4, l = 2)
hdMTD_FSC(X, d = 4, l = 3, alpha = 0.1)