We study regression models for nonstationary categorical time series and their applications, and address the issues of prediction, estimation and control. Generalized Linear Models and Partial Likelihood are the basic tools in the present study. The models link the probabilities of each category to a covariate process through a vector of time invariant parameters. Under mild regularity conditions, asymptotic properties of the estimators are established by appealing to martingale theory, and certain diagnostic tools are presented for checking the model adequacy. The methodology is demonstrated using real rainfall data. Subsequently we discuss a new recursive estimation method for time series following generalized linear models, motivated by the logistic regression model in conjunction with binary time series. The estimation procedure, suitably modified, gives rise to a stochastic approximation scheme used here to illustrate a connection between control theory and generalized linear models.