This thesis examines the statistical properties of the Poisson AR(1) model of Al-Osh and Alzaid (1987) and McKenzie (1988). The analysis includes forecasting,
estimation, testing for independence and specification and the addition of regressors to
the model.
The Poisson AR(1) model is an infinite server queue, and as such is well suited
for modeling short-term disability claimants who are waiting to recover from an injury or
illness. One of the goals of the thesis is to develop statistical methods for analyzing series
of monthly counts of claimants collecting short-term disability benefits from the
Workers' Compensation Board (WCB) of British Columbia.
We consider four types of forecasts, which are the k-step ahead conditional mean,
median, mode and distribution. For low count series the k-step ahead conditional
distribution is practical and much more informative than the other forecasts.
We consider three estimation methods: conditional least squares (CLS),
generalized least squares (GLS) and maximum likelihood (ML). In the case of CLS
estimation we find an analytic expression for the information and in the GLS case we find
an approximation for the information. We find neat expressions for the score function and
the observed Fisher information matrix. The score expressions leads to new definitions of
residuals.
Special care is taken to test for independence since the test is on the boundary of
the parameter space. The score test is asymptotically equivalent to testing whether the
CLS estimate of the correlation coefficient is zero. Further we define a Wald and
likelihood ratio test.
Then we use the general specification test of McCabe and Leybourne (1996) to
test whether the model is sufficient to explain the variation found in the data.
Next we add regressors to the model and update our earlier forecasting, estimation
and testing results. We also show the model is identifiable.
We conclude with a detailed application to monthly WCB claims counts. The
preliminary analysis includes plots of the series, autocorrelation function and partial
autocorrelation function. Model selection is based on the preliminary analysis, t-tests for
the parameters, the general specification test and residuals. We also include forecasts for
the first six months of 1995.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/8500 |
| Date | 05 1900 |
| Creators | Freeland, R. Keith |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Relation | UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/] |
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