厚尾GARCH模型之波動性預測能力比較

Comparison of the Volatility-Predicting Ability between Heavy-Tailed GARCH Models

10.29698/FJMR.200705.0003

李命志(Ming-Chih Lee)；洪瑞成(Jui-Cheng Hung)；劉洪鈞(Hung-Chun Liu)

GARCH ； 厚尾 ； 波動性預測 ； GARCH ； Fat-Tailed ； Volatility predicting

輔仁管理評論

14卷2期（2007 / 05 / 01）

47 - 71

繁體中文

本文分別以Gaussian GARCH模型、GARCH-GED模型、GARCH-HT模型，探討資產報酬率普遍存在高峰、厚尾現象時，何種分配的模型對於波動率具有較佳的相對預測能力。 實證結果顯示，在五種實證資料當中，GARCH-GED模型與GARCH-HT模型在不同條件平均數方程式假設下，相對預測能力都比Gaussian GARCH模型佳。GARCH-HT模型的相對預測能力則優於GARCH-GED模型。當以平均絕對誤差(MAE)作為評估準則，模型的優劣順序並沒有因為使用不同的衡量準則而發生改變。刪除極端值後，發現所有預測模型在不同條件平均數方程式設定下之MSE與MAE均明顯下降許多（除布朗特原油外），而重複進行DM檢定的結果亦指出模型的相對預測能力與刪除極端值之前的結論一致。特別的是，極端值確實會影響模型對波動性預測的績效。 本文採用移動視窗的方式進一步探討由Politis (2004)提出的厚尾分配與常見的GED分配再結合GARCH模型進行樣本外預測波動性的優劣。當改以同樣具備高峰、厚尾特性的GED分配與HT分配作比較時，更得以凸顯HT分配的優勢。再者，以DM檢定來呈現三種不同誤差項分配假設下GARCH(1,1)模型之間的相對預測能力亦較為恰當。

In this paper, Gaussian GARCH, GARCH-GED, and GARCH-HT (Politis, 2004) models are used to discuss the relative out-of-sample volatility predicting ability when the distribution of returns exhibits leptokurtic and fat-tailed. Empirical findings indicate that the relative out-of-sample volatility predicting ability of GARCH-GED model and GARCH-HT model are both superior to Gaussian GARCH model while GARCH-HT model performs better than GARCH-GED model under alternative conditional mean specifications. The performance ranking among these three models remains constant when using the mean absolute error (MAE) as the loss function. After removing outliers, except for Brent Europe, we found that both MSE and MAE have dropped substantially for all models and all conditional mean specifications. Meanwhile, the DM statistics show that the relative predictive ability is consistent with the result before removing outliers. Particularly, outliers certainly confound the relatively predictive performance. To sum up, this paper adopts rolling-window scheme to further examine out-of-sample volatility predicting ability among Gaussian GARCH, GARCH-GED and GARCH-HT models. In comparison with GED distribution, HT distribution reveals its predominance when returns exhibit leptokurtic and fat-tailed. Moreover, it is more appropriate to use DM test to demonstrate the relative out-of-sample volatility predicting ability among these three GARCH(1,1) models.

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