Statistical analysis of conditionally binomial nonlinear regression time series with discrete regressors

Abstract

The model of conditionally binomial nonlinear regression time series with discrete regressors is considered. A new frequencies-based estimator (FBE) of explicit form is constructed for this model. FBE is shown to be consistent, asymptotically normal, asymptotically effective, and to have less restrictive uniqueness assumptions w.r.t. the classical MLE. A fast recursive algorithm is constructed for FBE re-computation under model extension. An asymptotically optimal Wald test and forecasting statistic based on FBE are developed. Computer experiments on simulated data are performed for FBE.