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Statistica Sinica 9(1999), 153-166


THE WAVELET IDENTIFICATION OF THRESHOLDS AND TIME

DELAY OF THRESHOLD AUTOREGRESSIVE MODELS


Yuan Li and Zhongjie Xie


University of Petroleum and Peking University


Abstract: 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 see which have significantly large absolute values, the time delay is identified first. By further checking the empirical wavelets corresponding to the time delay across the fine scale levels, the thresholds and their number are identified. All estimators are shown to be strongly consistent.



Key words and phrases: Thresholds, time delay, wavelets.



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