HOMC: A MATLAB Package for Higher Order Markov Chains

We present a MATLAB package, which is the first of its kind, for Higher Order Markov Chains (HOMC). It can be used to easily compute all important quantities in our recent works relevant to higher order Markov chains, such as the \(k\) -step transition tensor, limiting probability distribution, ever-reaching probability tensor, and mean first passage time tensor. It can also be used to check whether a higher order chain is ergodic or regular, to construct the transition matrix of the associated reduced first order chain, and to determine whether a state is recurrent or transient. A key function in the package is an implementation of the tensor “box” product which has a probabilistic interpretation and is different from other tensor products in the literature. This HOMC package is useful to researchers and practitioners alike for tasks such as numerical experimentation and algorithm prototyping involving higher order Markov chains.