Robust Testing for GARCH by Wavelet Shrinkage

利用微波收縮建立GARCH效果的穩健統計檢定量

林信助(Shinn-Juh Lin)

《風險管理學報》 12卷2期 (2010/09) Pp. 235-256

https://doi.org/10.30003/JRM.201009.0004

摘要

瞭解波動度的本質有助於風險管理。例如風險值（Value at Risk）的計算便有賴於良好的波動度測度之建立。鑑於GARCH這一類模型在衡　量財務波動度上的普遍性，同時假定「對條件變異數作正確統計推論」是研究人員最關心的研究議題，本文探討在條件平均數式有可能被錯誤設定的前提之下，如何對GARCH效果作穩健的統計檢定。相關文獻上一個熟為人知的問題是：當條件平均數式設定有錯誤時，既使資料產生過程並不存在GARCH效果，但使用一個常被用來檢定GARCH效果的LM統計量來作檢定時，通常會過度拒絕沒有GARCH效果的虛無假設。在這篇文章中，我們利用微波收縮計算法來估計未知的條件平均數式，並據以提出一個穩健的GARCH效果統計檢定。微波收縮計算法的特色在於，它在移除雜訊的同時，會保留訊號其它非平滑的部分，例如大幅的跳動。我們的實驗結果顯示，微波收縮計算法確實可以顯著地移除因為非線性所造成的扭曲，同時也不會影響到統計量的檢定力。為了呈現實務關連性，我們利用此一統計量來檢定11/20/1985至12/7/1989的標準普爾500指數。我們的實證結果顯示，本文所提出的微波收縮計算法不僅可以成功的捕捉1987年十月股市崩盤所造成的結構性改變；它同時也防止研究人員在這種情況下錯誤拒絕沒有GARCH效果的虛無假設。這證實了本研究所提出的GARCH效果的穩健統計檢定量，確實有其實務上之關連性。

關鍵字

條件平均數式錯誤設定 ； 一般化自我回歸條件變異數異質性 ； 微波收縮

並列摘要

Understanding the nature of volatility is helpful in risk management. For example, the computation of the value at risk (VaR) relies critically on a good volatility measure. Given the popularity of the GARCH-type models in modeling financial volatility, we consider, in this paper, a robust testing for GARCH effect in the general context of a possibly mis-specified conditional mean, assuming that correct inference regarding the conditional variance is of primary interest to the researcher. It is well known in the literature that, when the conditional mean equation is mis-specified, the popular LM test for GARCH effect often leads to over-rejection of the null hypothesis of no GARCH, even when no such effect exists in the true data generating process. In this paper, we propose an alternative robust test of the GARCH effect by estimating the unknown conditional mean equation based on the wavelet shrinkage algorithm. An important feature of the wavelet shrinkage is its ability to remove noise while preserving non-smooth features, such as large spikes in the signal. Our experiments show that the wavelet shrinkage method indeed can significantly remove distortions introduced by nonlinearity without sacrificing the power of the test. To demonstrate the empirical relevance of the proposed test, we apply our robust test to study daily returns of the SP500 index from 11/20/1985 to 12/7/1989. Our result shows that the wavelet shrinkage method proposed here not only successfully picks up the structural change caused by the October 1987 stock market crash, it also prevent researchers from falsely rejecting the null of no GARCH effect in such a situation. This demonstrates the practical relevance of the robust test proposed in this research.

並列關鍵字

Conditional Mean Mis-specification ； Generalized Autoregressive Conditional Heteroscedasticity ； Wavelet Shrinkage

參考文獻

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