Estimation of an autoregressive semiparametric model with exogenous variables (Q1299534)

The authors deal with the estimation of an autoregressive semiparametric model \[ X_{t+1}= \varphi(X_t, \dots,X_{t-r+1})+ \psi(Y_t)+ \varepsilon_t, \] where \(\varphi\) and \(\psi\) are unknown nonlinear functions and \(\{Y_t\}\) is an exogenous variable. Two special cases are considered: (1) \(\psi\) is linear \(\psi(Y_t)= AY_t\) with an unknown parameter \(A\); (2) \(\psi\) is nonlinear corresponding to a series expansion. One first estimates parametrically the exogenous part \(\psi(\cdot)\), and then estimates nonparametrically the endogeneous part \(\varphi(\cdot)\). The a.s. and \(L_s\) convergence results are given. Numerical simulations demonstrate the method.