Asymptotic analysis of non-stationary functional series TAR estimators

Functional Series Time-dependent AutoRegressive (FS-TAR) models constitute an important class of models for non-stationary signal modelling. However, the asymptotic properties of "general" (not necessarily periodically evolving) FS-TAR estimators are not, yet, well understood. In the present study, the problem of establishing an asymptotic analysis framework capable of accounting for "general" FS-TAR estimators is considered. The proposed framework is used for deriving the asymptotic properties of the "general" FS-TAR Weighted Least Squares (WLS) estimator, while the validity of the asymptotic analysis results is confirmed through Monte Carlo experiments.