Wavelets are applied to detect the jumps in a heteroscedastic autoregressive model. The empirical wavelet coefficients are defined respectively for the conditional mean and the conditional variance of the model. It is shown that the wavelet coefficients exhibit high peaks near the jump points,...

Wavelets are applied to identify the time delay and thresholds in open-loop threshold autoregressive models. Based on Truong and Stone's lemma, the empirical wavelet coefficients of the data are defined. The time delay and thresholds are detected and then estimated by checking the variation of...

In this paper, we propose a diagnostic technique for checking heteroscedasticity based on empirical likelihood for the partial linear models. We construct an empirical likelihood ratio test for heteroscedasticity. Also, under mild conditions, a nonparametric version of Wilk's theorem is derived,...