Partial Likelihood Analysis of Time Series Models, with Application to Rainfall-Runoff Data,
MARYLAND UNIV COLLEGE PARK DEPT OF MATHEMATICS
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A general logistic-autoregressive model for binary time series or longitudinal responses is presented, generalizing the discrete-time Cox 1972 model with time-dependent covariates as well as the recent regression models of Kaufmann 1987 for categorical time-series. Since this model is formulated in terms of the time-series covariates which are not themselves explicitly modelled, the large-sample theory of parameter-estimation must be justified by means of Partial Likelihood in the sense of Cox 1975, using theoretical results like those of Wong 1986. The large-sample theory also justifies goodness of fit tests analogous to the chi-squared tests of Schoenfeld 1980 and to the tests based on sums of normalized squared residuals used in logistic regression. These ideas are illustrated by analysis of a rainfall-runoff hydrological dataset previously analyzed by Yakowitz 1987.
- Numerical Mathematics