Statistical Estimation of Parameters for Binary Conditionally Nonlinear Autoregressive Time Series

The problem of statistical parameter estimation is considered for binary GLM-based autoregression with the link function of general form and the base functions (regressors) nonlinear w.r.t. the lagged variables. A new consistent asymptotically normal frequencies-based estimator (FBE) is constructed and compared with the classical MLE. It is shown that the FBE has less restrictive sufficient conditions of uniqueness than the MLE (does not need log-concavity of the inverse link) and can be computed recursively under the model extension. The sparse version of the FBE is proposed and the optimal model-dependent weight matrices (parameterizing the FBE) are found for the FBE and for the sparse FBE. The proposed empirical choice of the subset of s-tuples for the sparse FBE is examined by numerical and analytical examples. Computer experiments for comparison of the FBE versus the MLE are performed on simulated and real (genetic) data.