GARCH族模型的波動(dòng)率預(yù)測(cè)績(jī)效比較分析報(bào)告

1、. .圖3可以看出，以MSE和MAE為衡量指標(biāo)，EGARCH的預(yù)測(cè)績(jī)效不與APARCH；而以MAPE和HMSE為指標(biāo)，則情況剛好相反。利用OLS方法將此二者的預(yù)測(cè)績(jī)效進(jìn)行比較，四種損失函數(shù)的相對(duì)績(jī)效并無(wú)顯著差異，回歸的p值分別為0.324（MSE）、0.716（MAE）、0.430（MAPE）和0.362（HMSE）。因此，可以認(rèn)為EGARCH和APARCH模型的預(yù)測(cè)績(jī)效無(wú)顯著差異。除EGARCH模型之外，APARCH模型與其它模型相比，最重要的改進(jìn)是模型刻畫的是條件方差的次冪的動(dòng)態(tài)過(guò)程。然而，從模型的構(gòu)造來(lái)看，的動(dòng)態(tài)過(guò)程對(duì)于EGARCH模型來(lái)講，相當(dāng)于方程兩邊同時(shí)乘以系數(shù)。此時(shí)，EGARCH

2、模型所刻畫的即為取對(duì)數(shù)之后的動(dòng)態(tài)過(guò)程。與APARCH相比，主要差異僅在于前一期的新息對(duì)條件方差的影響。但這種差異并未改變EGARCH和APARCH模型的一個(gè)共同特征，即前一期的新息會(huì)增加下一期波動(dòng)，而且的符號(hào)對(duì)的影響是非對(duì)稱的。另外，考慮到波動(dòng)過(guò)程往往具有較強(qiáng)的持續(xù)性，主要受到的影響（GARCH項(xiàng)的系數(shù)通常遠(yuǎn)大于ARCH項(xiàng)和非對(duì)稱項(xiàng)）。因此，直觀上來(lái)看，EGARCH和APARCH模型對(duì)收益率的波動(dòng)過(guò)程具有類似的刻畫能力。5 結(jié)論與其它異方差模型相比，GARCH族模型形式簡(jiǎn)潔、易于操作，而且能夠較好地刻畫收益率的波動(dòng)過(guò)程。因此，在很多金融理論和實(shí)踐領(lǐng)域，GARCH族模型都有著重要的應(yīng)用。自上世紀(jì)

3、80年代以來(lái)，GARCH族模型得到了極大的豐富。學(xué)者們基于理論和經(jīng)驗(yàn)結(jié)果發(fā)展了各種GARCH類結(jié)構(gòu)。然而，豐碩的成果卻給人們?cè)趯?shí)際應(yīng)用時(shí)帶來(lái)了新的困惑：究竟哪種設(shè)定能夠較好地描述收益率的波動(dòng)過(guò)程呢？為了回答這一問(wèn)題，本研究從波動(dòng)性預(yù)測(cè)的角度，對(duì)10種常見的GARCH族模型進(jìn)行了實(shí)證比較。鑒于正態(tài)分布假設(shè)下的極大似然估計(jì)（準(zhǔn)極大似然估計(jì)，QMLE）效率較差（可能會(huì)引起績(jī)效評(píng)價(jià)產(chǎn)生偏差），而其它的參數(shù)化模型又可能存在“模型風(fēng)險(xiǎn)”，本研究采用一種半?yún)?shù)方法估計(jì)函數(shù)（Estimating Function）方法進(jìn)行參數(shù)估計(jì)。由于金融資產(chǎn)的收益率常常表現(xiàn)出顯著的偏斜和超額峰度，估計(jì)函數(shù)方法在進(jìn)行參數(shù)估計(jì)

4、時(shí)引入了這些高階矩信息，因此，比QMLE具有更高的估計(jì)效率。另外，在進(jìn)行績(jī)效評(píng)價(jià)時(shí)，傳統(tǒng)的對(duì)損失函數(shù)排序的方法不能給出一個(gè)統(tǒng)計(jì)意義下的結(jié)果，且可能存在“數(shù)據(jù)窺察”（Data Snooping）問(wèn)題，本文分別使用最小二乘（OLS）方法和“優(yōu)越的預(yù)測(cè)能力”（SPA）檢驗(yàn)進(jìn)行研究。在選取“模型全集”時(shí)，與現(xiàn)有研究不同，本文首先使用樣本擬合的方法確定模型的均值方程形式以與方差方程的滯后期，然后保持這些設(shè)定不變，使用不同的GARCH類結(jié)構(gòu)進(jìn)行波動(dòng)性預(yù)測(cè)，以期得到相對(duì)“純凈”的因GARCH結(jié)構(gòu)的不同而引起的預(yù)測(cè)績(jī)效的不同。鑒于QMLE是現(xiàn)有研究常用的方法，為了進(jìn)行比較，本研究也對(duì)該估計(jì)方法進(jìn)行了考查。結(jié)果

5、與現(xiàn)有研究不同，在正態(tài)分布的假設(shè)下，形式最簡(jiǎn)潔的積分GARCH（IGARCH）模型具有較好的預(yù)測(cè)績(jī)效。然而，基于估計(jì)函數(shù)方法的預(yù)測(cè)績(jī)效表明，指數(shù)GARCH（EGARCH）和非對(duì)稱冪GARCH（APARCH）模型的預(yù)測(cè)能力更加優(yōu)越。由于估計(jì)函數(shù)方法具有更高的估計(jì)效率，因此，與其它GARCH類模型相比，本文認(rèn)為EGARCH和APARCH模型能夠更好地描述金融資產(chǎn)收益率的波動(dòng)過(guò)程。參考文獻(xiàn)Bollerslev T. Generalized autoregressive conditional heteroskedasticityJ. Journal of Econometrics, 1986, 31

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19、onsistent ranking of volatility modelsJ. Journal of Econometrics, 2006, 131(1-2): 97-121.Comparing the performances of volatility prediction from GARCH-type modelsFANG Libing1, KUO Biingshen2, ZENG Yong11. School of Management and Economics, University of Electronic Science and Technology of China,

20、Chengdu610054, China2. Department of International Trade, NationalChengchiUniversity, Taipei 11605Abstract：The GARCH family has been greatly flourished during the past two decades. However, this fact introduces a new important question. Which member of the family can not be outperformed? The present work samples daily returns from Chinese stock