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One-Sided Testing For Arch Effects Using Wavelets

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  • Hong, Yongmiao
  • Lee, Jin
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    Abstract

    There has been increasing interest recently in hypothesis testing with inequality restrictions. An important example in time series econometrics is hypotheses on autoregressive conditional heteroskedasticity (ARCH). We propose a one-sided test for ARCH effects using a wavelet spectral density estimator at frequency zero of a squared regression residual series. The square of an ARCH process is positively correlated at all lags, resulting in a spectral mode at frequency zero. In particular, it has a spectral peak at frequency zero when ARCH effects are persistent or when ARCH effects are small at each individual lag but carry over a long distributional lag. As a joint time-frequency decomposition method, wavelets can effectively capture spectral peaks. We expect that wavelets are more powerful than kernels in small samples when ARCH effects are persistent or when ARCH effects have a long distributional lag. This is confirmed in a simulation study.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 17 (2001)
    Issue (Month): 06 (December)
    Pages: 1051-1081

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    Handle: RePEc:cup:etheor:v:17:y:2001:i:06:p:1051-1081_17

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    Cited by:
    1. Francq, Christian & Zakoian, Jean-Michel, 2008. "Testing the nullity of GARCH coefficients : correction of the standard tests and relative efficiency comparisons," MPRA Paper 16672, University Library of Munich, Germany.
    2. Ho, Kin Yip & Tsui, Albert K.C., 2004. "Analysis of real GDP growth rates of greater China: An asymmetric conditional volatility approach," China Economic Review, Elsevier, vol. 15(4), pages 424-442.
    3. Li, Linyuan & Yao, Shan & Duchesne, Pierre, 2014. "On wavelet-based testing for serial correlation of unknown form using Fan’s adaptive Neyman method," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 308-327.
    4. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1305-1331, October.
    5. 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.
    6. Duchesne, Pierre, 2006. "Testing for multivariate autoregressive conditional heteroskedasticity using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2142-2163, December.

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