尋找合理的變數幫助預測大盤波動走勢

本文欲探討外生之總體變數是否能幫助 GARCH 模型之波動率預測，除此之外，我們也加入了一些文獻中常見的變數來探討其對波動模型之影響。文中納入了不同種類的 GARCH 模型，包括了常見的不對稱 GARCH 模型，以期能做出較為完善的比較。本文選擇以美國 S&P 500指數之報酬波動率為預測對象，而資料頻率則包括了日資料與週資料。最後，本文也嘗試了將特定的變數以主成份分析與 HELP method 進行資料縮減，得出新的波動變數後，並一同與原始的變數進行綜合比較。實證結果發現不對稱的 GARCH 模型在資料配適上較對稱 GARCH 模型為佳，特別是 EGARCH 模型表現最好。然而，若考量模型的預測能力，EGARCH 模型顯然有過度配適的問題。而 GJR-GARCH 模型的預測能力為最佳，配適能力則依據資料頻率而有所差異，但仍勝過對稱的 GARCH 模型。在外生變數方面，整體而言，貨幣供給 (M1)、三個月期國庫券市場利率 (3-month treasury bill rate) 與10年期的政府公債利率 (10-year treasury constant maturity rate) 和聯邦資金利率 (federal fund rate) 對於模型有較顯著的幫助。但是，VIX、市場交易量和油價等變數，對模型而言並無顯著的績效提昇。另一方面，主成份分析和HELP method 並未能顯著的改善預測績效，僅有在特定的模型與資料頻率下才能對模型有所幫助。總言之，我們發現日資料的波動率相對不易以加入外生變數來獲得更好的預測結果；然而，週資料的波動率則較容易被外生變數所預測。

關鍵字

GARCH ；波動率；預測；總體變數；主成份分析；資料縮減

並列摘要

This paper aims to examine if incorporating exogenous macro variables can help forecast stock market volatility via GARCH-class models, and if some popular variables can improve the forecasting performances. We utilize various GARCH models, including asymmetric ones, for comprehensive comparisons. In addition, We also use data-reduction method, such as principal component analysis and HELP method, to generate new volatility variables to see the effects they bring. Empirical results show that asymmetric GARCH model and GJR-GARCH, not only do good job of fitting data, but provide better forecasting performances. However, EGARCH apparently suffers from the problem of over-fitting, and it gives worst forecasts among these models. In general, the inclusion of M1 money supply, 3-month treasury bill rate, 10-year treasury constant maturity rate and federal fund rate do help the GARCH models significantly; in contrast, VIX, trading volume and oil price do not work well. In addition, both PCA and HELP method are unable to enhance the performance of models, and they merely work under certain conditions. We also find that the forecasting performances of daily volatility are more difficult to be improved by employing exogenous variables and using different GARCH models compared to weekly volatility.