比較GARCH跳躍模型並運用日本、美國及台灣指數實證分析

Abstract

本論文主要為研究GARJI模型，在利用”隨時間變化”之跳躍頻率(Jump intensity)及跳躍大小(Jump size)，相較於其他模型是否有較好的波動度預測能力，並以跨國的資料做比較，看其成效如何。 除了使用GARJI模型以外，本文另外加入了混合型GARCH跳躍模型及GARCH(1,1)模型相比較其對市場報酬率的配適能力。接著使用四種統計方法來判斷其表現能力。第一種為均方誤差(MSE)。第二種為均方根誤差(RMSE)。第三種為平均絕對誤差(MAE)。第四種為效用函數(Utility function)。在利用各種模型預測出波動度之後，再將其波動度與利用市場日內報酬率所計算出之已實現波動度跑迴歸，並判斷各種模型的R-square大小，進而說明其對波動度預測能力的好壞。 根據研究結果指出，GARJI對於市場報酬率發生大幅度波動時，比其他模型有較強的解釋能力。傳統其他模型並無法應對突發的大幅度波動改變狀況。但是GARJI模型可將其波動度的不規則變化分成兩種因素，當波動度以平滑小幅度變動時，以基本GARCH因子配適，而在大幅度變動則以跳躍因子配適。 最後我們以各種模型運用在各國市場做實證比較，結果發現在S&P500指數上，GARJI模型對於樣本外之預測能力皆優於其他模型，利用效用函數所計算出之效用值也最高。

This paper uses three models to fit volatility of market return. The main model is GARJI model, it has better forecasting performance than any other models, because it fits the return volatility by considering the components of “jump intensity” and “jump size”. These two components have a special property which is time-varying. GARJI has this important property so that GARJI is much better than others.

We compare the realized volatility with conditional volatilities, which are computed by these three models：GARJI、mixed GARCH constant jump and GARCH(1,1). After that we check the forecasting ability by four criterion. The first one is Mean Squared Error(MSE); the second is Root of Mean Squared Error; the third is Mean absolute Error(MAE); the last one is utility function.

Finally, in this paper, we conclude that GARJI is the best model of the three. Its forecasting ability on out of sample on S&P500 index is much better than others. Besides, the utility of GARJI is also the highest.