Estimation of a multiple-threshold AR(p) model

The present paper deals with the multiple-threshold pp-order autoregressive model which has been introduced by Tong and Lim [H. Tong, K.S. Lim, Threshold autoregression, limit cycles and cyclical data, J. R. Stat. Soc. Ser. B 42 (1980) 245–292] in nonlinear system modelling. Under some conditions on the coefficients of the model which ensure the stationarity, the existence of moments and the strong mixing property of this process and under other mild assumptions, we establish the asymptotic properties (consistency and asymptotic normality) of the minimum Hellinger distance estimates of the autoregressive coefficients of the model.