The wavelet identification of thresholds and time delay of threshold autoregressive models

In this paper, we consider identification of the thresholds and time delay of threshold autoregressive models with p- dependence and an unknown number of thresholds. By checking p different empirical wavelets of the data to s ee which have significantly large absolute values, the time delay is identi fied first. By further checking the empirical wavelets corresponding to the time delay across the fine scale levels, the thresholds and their number a re identified. All estimators are shown to be strongly consistent.