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Statistica Sinica 17(2007), 265-287



Yingcun Xia, Wai-Keung Li and Howell Tong

National University of Singapore, University of Hong Kong and
London School of Economics

Abstract: Selecting the threshold variable is a key step in building a generalized threshold autoregressive (TAR) model. This paper proposes a semi-parametric method for this purpose that is based on a single-index functional coefficient model. The asymptotic distribution of the estimator is obtained. A simple algorithm is given and its convergence is proved. Some simulations are reported. Two data sets are analyzed, one of which gives strong statistical support for ratio-dependent predation in Ecology.

Key words and phrases: Local linear smoother, nonlinear time series, single-index coefficient models, threshold autoregressive (TAR) time series models.

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