短期利率波動度動態中的不對稱與長記憶現象

Asymmetry and Long Memory in the Dynamics of Interest Rate Volatility

本研究同時檢驗短期利率波動度動態中的條件異質變異效果與長記憶效果，以三個月期的美國政府公債利率為樣本，分別藉由GARCH、EGARCH以及FIEGARCH模型來估計短期利率波動度的參數，並比較模型之表現。結果顯示，同時包含不對稱波動度與長記憶波動度效果的FIEGARCH模型表現最佳，特別是對於月資料的預測。顯示短期利率波動度同時具有不對稱與長記憶的特性，故過去文獻上僅單獨考慮不對稱或長記憶效果實有不足。另外，本研究亦比較短期利率模型中，漂移項（drift term）的不對稱與非線性設定在模型解釋力上的差異。結果顯示，相較於非線性設定，漂移項的不對稱設定較能顯著提高模型的解釋力，表示短期利率漂移項存在不對稱的均數回歸（mean-reverting）現象，但並無非線性效果。

The conditionally heteroskedastic volatility effect in the short-rate volatility process has been broadly investigated, and the long memory phenomena has attracted a lot of attentions, too. However, these two effects have never been involved together to model the dynamics of short-rate volatility. We introduce an asymmetry and long memory conditional variance model, FIEGARCH, to model the dynamics of short-term interest rate volatility on three-month U.S. Treasury bills. By finding significant estimates, we recognize the necessity of the asymmetric volatility function with the long memory property. Our results also show that non-linearity is not a necessary fact for the short-rate drift, instead, the asymmetric specification plays an important role in the mean function. Finally, according to the comparison for the prediction of the volatility dynamics, the FIEGARCH shows better forecasting ability, especially for a monthly frequency.