Physical Sciences and Mathematics Commons^™

Count Time Series And Discrete Renewal Processes, James Livsey

All Dissertations

Most data collected over time has some degree of periodicity (i.e. seasonally varying
traits). Climate, stock prices, football season, energy consumption, wildlife sightings, and
holiday sales all have cyclical patterns. It should come as no surprise that models that
incorporate periodicity are paramount in the study of time series.
The following work devises time series models for counts (integer-values) that are periodic
and stationary. Foundational work is rst done in constructing a stationary periodic
discrete renewal process (SPDRP). The dynamics of the SPDRP are mathematically interesting
and have many modeling applications, expositions largely unexplored here. This work
develops a SPDRP …