Moment estimation of uncertain threshold autoregressive model

As a type of non linear uncertain time series model, the uncertain threshold autoregressive model serves as a powerful tool for modeling time series systems with non linear frameworks caused by state transitions. To further expand the applied research on the uncertain threshold autoregressive model, this article first constructs a statistical invariant based on its threshold characteristics and uncertain disturbance terms. On this basis, this article also proposes the moment estimation for the uncertain threshold autoregressive model and designs a numerical algorithm to solve the numerical solution of the moment estimation. To verify the suitability of the estimated uncertain threshold autoregressive model, the article further introduces the residuals and scale residuals of the estimated model and investigates its uncertain hypothesis testing problem as well as point forecast and interval forecast problems based on the above results. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.