Regression models for binary time series

Abstract

We consider the general regression problem for binary time series where the covariates are stochastic and time dependent and the inverse link is any differentiable cumulative distribution function. This means that the popular logistic and probit regression models are special cases. The statistical analysis is carried out via partial likelihood estimation. Under a certain large sample assumption on the covariates, and owing to the fact that the score process is a martingale, the maximum partial likelihood estimator is consistent and asymptotically normal. From this we obtain the asymptotic distribution of a certain useful goodness of fit statistic.