Testing and estimation of thresholds based on wavelets in heteroscedastic threshold autoregressive models

We consider the testing and estimation of thresholds in heteroscedastic threshold autoregressive models with an unknown number of thresholds. A test statistic based on empirical wavelet coefficients is proposed.The asymptotic distribution of the test statistic is established and consistent estimators of the thresholds and the number of thresholds are given. A Monte Carlo study and a real example are used to assess the performance of our method.