The bounded-memory right-corner HHMM described in this article can also be lexicalized in this way, but because head word dependencies are most straightforwardly defined in terms of top-down PCFG-like dependency structures, this lexicalization requires the introduction of additional formal machinery to transform PCFG probabilities into right-corner form (Schuler 2009).
rather than transforming a training set of trees and mapping them to a time series model, it is necessary to transform a consistent probabilistically weighted grammar (in some sense, an infinite set of trees) into appropriately weighted and consistent right-corner PCFG and HHMM models.