There is a need for the development of models that are able to account for discreteness in data, along with its time series properties and correlation. A review of the application of thinning operators to adapt the ARMA recursion to the integer-valued case is first discussed. A class of integer-valued ARMA (INARMA) models arises from this application. Our focus falls on INteger-valued AutoRegressive (INAR) type models. The INAR type models can be used in conjunction with existing model-based clustering techniques to cluster discrete valued time series data. This approach is then illustrated with the addition of autocorrelations. With the use of a finite mixture model, several existing techniques such as the selection of the number of clusters, estimation using expectation-maximization and model selection are applicable. The proposed model is then demonstrated on real data to illustrate its clustering applications. / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/22275 |
| Date | January 2017 |
| Creators | Roick, Tyler |
| Contributors | McNicholas, Paul D., Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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