Spontaneous speech of healthy adults consists of alternating periods of fluent and hesitant segments, forming temporal cycles in speech fluency. The regularity of these cycles may be related to the functioning of brain networks during speech planning and execution. This paper investigates the theoretical link between human cognitive functioning and temporal cycles in speech production using a quantitative time series analysis to characterize the regularity and frequency of temporal cycles in adults with differing levels and etiology of cognitive decline. We compare spontaneous speech of adults without a neurological diagnosis, both older and younger, to that of adults with frontotemporal lobar degeneration (FTLD). Two measures of temporal cycle frequency (mean and mode) calculated from the power spectrum of speech fluency represented as a time series were found to be associated with subjects' age, regardless of diagnosis of dementia. Two measures of periodicity (g-statistic and rhythmicity-index), as well as mean frequency, differentiated between adults with and without dementia. Our study confirms the presence of regular temporal cycles in spontaneous speech and suggests that temporal cycle characteristics are affected in different ways by declines in cognitive functioning due to dementia and aging.