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...

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,...

A wavelet method is applied to the detection of the hidden periodicities of a hidden periodic model in time series. By checking the empirical wavelet coefficients of the periodogram, which have significantly large absolute values across fine scale levels, the number of the hidden periodicities...