  Long-range correlation, a property of time series exhibiting long-term
memory, is mainly studied in the statistical physics domain and has been
reported to exist in natural language. Using a state-of-the-art method for such
analysis, long-range correlation is first shown to occur in long CHILDES data
sets. To understand why, Bayesian generative models of language, originally
proposed in the cognitive scientific domain, are investigated. Among
representative models, the Simon model was found to exhibit surprisingly good
long-range correlation, but not the Pitman-Yor model. Since the Simon model is
known not to correctly reflect the vocabulary growth of natural language, a
simple new model is devised as a conjunct of the Simon and Pitman-Yor models,
such that long-range correlation holds with a correct vocabulary growth rate.
The investigation overall suggests that uniform sampling is one cause of
long-range correlation and could thus have a relation with actual linguistic
processes.
