Language is passed from one generation of learners to the next via cultural transmission. This process has been shown to give rise to core properties of language that enhance its learnability. Recent experimental work shows that statistical properties of language can also emerge through cultural transmission: specifically, the statistical coherence of words, and the Zipfian distribution of word frequencies. It has been proposed that these properties emerge because they facilitate segmentation. However, it is not clear whether segmentation is necessary for their emergence. We use a computational iterated learning model to simulate the cultural transmission of unsegmented sequences under different assumptions about the nature of learning. We show that segmentation indeed promotes the emergence of these statistical properties, whereas tracking of unigram statistics does not. In addition, we show that tracking sequential statistics alone can also promote their emergence.