Abstract
Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model xt = T(xt−1) + ɛt. By checking the empirical wavelet coefficients of the data, which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method is also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given, which are shown to be consistent.
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