在本文中,我們使用台灣加權股價指數、日本Nikkei 225指數和美國S&P 500指數週資料,來比較BEKK模型、Diagonal BEKK模型、CCC模型、報酬基礎DCC模型和變幅基礎DCC模型對相關係數與共變異數進行市場交易資料的樣本內預測能力之比較。首先,進行標準化殘差的自我相關檢定,結果顯示相對於其他模型,變幅基礎DCC是較好的模型。同時使用平均絕對誤差(MAE, mean absolute error)和均方根誤差(RMSE, root mean squared error)兩種誤差函數指標來進行相關係數與共變異數在預測能力高低方面的比較分析,並引用五種不同實現的(realized)相關係數做為真實相關係數的代理變數,以當做預測績效評比的不同指標。實證結果發現在不同的情況下,預測績效似乎不具有一致性,亦即沒有一個模型在不同預測績效評比指標下是絕對優於其他模型。在相關係數的預測方面,以D_BEKK模型的表現最好。在共變異數的預測方面,仍然是以D_BEKK模型的表現最好,其次是報酬基礎之下的I_DCC模型。另外,單就DCC族的模型進行比較,發現變幅基礎DCC模型在相關係數的預測上明顯優於報酬基礎DCC模型,不過在共變異數的預測上則沒有明顯的差異。
We use stock market index to compare in-sample prediction performance of BEKK model, Diagonal BEKK model, CCC model, Return-based DCC model, and Range-based DCC model. The sample is weekly return and range of Taiwan weighted stock index, Nikkei 225 index, and S&P 500 index. We implement diagnostic test for autocorrelation of standardized residual, and the results show that all models are misspecified, but the range-based DCC model is better than others. Moreover, we apply the error function including MAE and RMSE to analyze the prediction performance of correlation coefficient and covariance, and develop five kinds of realized correlation coefficient for comparison benchmark. Furthermore, empirical results of the prediction performance by these models seem to be inconsistent, and we find that Diagonal BEKK model outperforms others for prediction correlation coefficient and covariance. In DCC type model comparison aspect, we find that range-based DCC model is better than return-based DCC model in correlation coefficient forecasts. However, there are not significantly different in forecasting for covariance.