Abstract: A general logistic autoregressive model for binary time series that takes into account stochastic time dependent covariates is presented, and its large sample theory is studied via partial likelihood inference in the sense of Cox (1975) and Wong (1986). The maximum partial likelihood estimator is consistent and asymptotically normal under some conditions on the asymptotic behavior of the time dependent covariates. This leads to asymptotic results concerning several goodness of fit and test statistics. Some of these statistics are applied in logistic regression analysis of level-upcrossings of runoff data using rainfall as covariate data.
Key words and phrases: Maximum partial likelihood estimator, asymptotic efficiency, information matrix, empirical measure, goodness of fit, martingale.