Abstract:

Wavelets are applied to detection of the jump points of a regression function
in nonlinear autoregressive model x_t=T(x_t-1)+ε_t.
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.

Key words:  Jump points, nonlinear autoregressive models, wavelets