波動預測績效比較－變幅為基礎 vs.報酬率為基礎

Comparison of Volatility Forecasting Performance-Range-Based Method vs. Return-Based Method

邱建良(Chien-Liang Chiu) ； 洪瑞成(Jui-Cheng Hung) ； 章育瑄(Yu-Hsuan Chang)

《績效與策略研究》 8卷2期 (2011/10) Pp. 31-48

https://doi.org/10.6736/JPSR.201110_8(2).0003

摘要

本研究主要探討九個不同國家的股價指數：KOSPI（韓國KOSPI股價指數）、NKI225（日經225股價指數）、TAIEX（台灣加權股價指數）、DJIA（美國道瓊工業股價指數）、NDX（美國那史達克股價指數）、SPX（美國S&P500股價指數）、CAC（法國CAC40股價指數）、FTSE（英國FTSE100股價指數）及DAX（德國DAX30股價指數）波動度的特性，除了運用變幅單一變數來預測外，還將其拆成最高價及最低價二個變數，且分別利用ARMA模型、GARCH模型、CARR模型與VECM模型等不同波動度模型中配適出較適合各國股價指數波動度的模型。再者，本研究採用Parkinson（1980）之變幅波動（range volatility）及報酬平方（squared return）作為真實波動度代理變數，並利用MSE、MAE、LLE、GMLE等四種統計損失函數（loss function）及VaR財務績效評估，分別作為預測能力衡量指標，最後以SPA檢定各模型預測能力之優劣。實證結果為：當決策者使用MAE與LLE為損失函數時，則用CARR模型有較佳的預測能力；當決策者使用MSE與GMLE為損失函數時，則用不對稱GARCH模型有較佳的預測能力。當決策者使用VaR財務績效評估時，除了KOSPI、NKI225和TAIEX是以不對稱GARCH模型有較佳的預測能力外，其餘股價指數皆是以CARR模型有較佳的預測能力。整體而言，由統計之觀點與財務之觀點來看波動度預測能力會得到相同的結論，各國股價指數不是以CARR模型預測較佳，就是以不對稱GARCH模型預測較佳。

關鍵字

GARCH模型 ； 變幅 ； 變幅波動 ； SPA test

並列摘要

This article selects the appropriate model to match volatility of nine stock markets from ARMA, GARCH, CARR and VECM models and use range, high and low variables to match the models. In the meantime, we use Parkinson (1980) proposed ranged-based estimator and squared return to be the proxy of true volatility. This study not only uses statistic loss functions, including MAE, MSE, LLE, GMLE and the VaR performance assessments are based on the range of measures that address the accuracy and efficiency, but also employ more robust SPA test to compare forecasting performance of models. The empirical result indicates that, for MAE and LLE, CARR model is preferred. In addition, for MSE and GMLE, asymmetric GARCH models are preferred. For VaR based loss function, except for KOSPI, NKI225 and TAIEX, CARR model is preferred. In a word, for statistic and financial loss functions, there are high performance to forecast volatility of nine stock markets which is CARR model or asymmetric GARCH model be used. Therefore, alternative stock markets and loss functions are important for volatility forecasting.

並列關鍵字

GARCH models ； Range ； Range-Based Volatility ； SPA t

參考文獻

周雨田、巫春洲、劉炳麟(2004)。動態波動模型預測能力之比較與實證。財務金融學刊。13(1)，1-25。

Alizadeh, S,Brandt, M.,Diebold, F.(2002).Range-based estimation of stochastic volatility models.Journal of Finance.57,1047-1091.

Andersen, T. G.,Bollerslev, T.(1998).Answering the skeptics: Yes, standard volatility models do provide accurate forecasts.International Economic Review.39(4),885-905.

Beckers, S.(1983).Variances of security price returns based on high, low, and closing prices.Journal of Business.56,97-112.

Black, F.(1976).Studies of stock price volatility changes, Proceedings of the 1976 meetings of the American statistical association.Business and Economics Statistics Section.177-181.