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Threshold variable selection by wavelets in open-loop threshold autoregressive models

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  • Ip, Wai-Cheung
  • Wong, Heung
  • Li, Yuan
  • Xie, Zhongjie

Abstract

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 the empirical wavelet coefficients. All the estimators are shown to be consistent.

Suggested Citation

  • Ip, Wai-Cheung & Wong, Heung & Li, Yuan & Xie, Zhongjie, 1999. "Threshold variable selection by wavelets in open-loop threshold autoregressive models," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 375-392, May.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:4:p:375-392
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    References listed on IDEAS

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    1. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    2. M. B. Priestley, 1980. "State‐Dependent Models: A General Approach To Non‐Linear Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 47-71, January.
    3. Rong Chen, 1995. "Threshold Variable Selection In Open‐Loop Threshold Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 461-481, September.
    4. Young K. Truong & Charles J. Stone, 1994. "Semiparametric Time Series Regression," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 405-428, July.
    5. Li, Yuan & Xie, Zhongjie, 1997. "The wavelet detection of hidden periodicities in time series," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 9-23, August.
    6. Cathy W. S. Chen & Jack C. Lee, 1995. "Bayesian Inference Of Threshold Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(5), pages 483-492, September.
    7. John Geweke & Nobuhiko Terui, 1993. "Bayesian Threshold Autoregressive Models For Nonlinear Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 441-454, September.
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    Cited by:

    1. Cathy Chen & Feng-Chi Liu & Mike So, 2013. "Threshold variable selection of asymmetric stochastic volatility models," Computational Statistics, Springer, vol. 28(6), pages 2415-2447, December.
    2. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2008. "Detections of changes in return by a wavelet smoother with conditional heteroscedastic volatility," Journal of Econometrics, Elsevier, vol. 143(2), pages 227-262, April.
    3. Zhou, Yong & Wan, Alan T.K. & Xie, Shangyu & Wang, Xiaojing, 2010. "Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 183-201, November.

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    Keywords

    Time delay Thresholds Wavelets;

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