# 臺灣博碩士論文加值系統

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 本研究使用具有GARCH效應的網絡自迴歸模型(簡記為NAR-GARCH)，來描述不同市場指數的連帶變動。首先藉由邊際模型過濾掉每個指數本身具有的GARCH效應並取得標準化殘差。再藉由NAR模型與定義一合適的鄰接矩陣對標準化殘差建模以容納其他指數的最新資訊。我們提出使用格蘭傑因果檢定判定不同指數之間的滯後互相關，在有滯後互相關的影響下，進一步測試在急劇上升或下降時的滯後相關性是否顯著用以建構鄰接矩陣。我們將NAR-GARCH模型應用於2006年到2020年的20個全球股價指數之對數報酬並探討其預測表現。數值結果顯示出NAR-GARCH模型在指數發生急劇上升或下降時，具有特別出色的預測結果。
 This study employs a network autoregressive model with GARCH effects, denoted by NAR-GARCH, to describe the dynamics of different market indices jointly. We propose to filter out the GARCH effects inherent in each index and obtain the associated standardized residuals marginally at first. A NAR model with the standardized residuals is adopted to accommodate other indices' most updated information by defining a suitable adjacency matrix. We propose using the Granger causality test to determine the lags of cross correlations between different indices and further testing whether the correlations of sharp upward or downward movements associated with the lags are significant for constructing the adjacency matrix. We apply the NAR-GARCH model to the log-returns of 20 global stock indices from 2006 to 2020 and investigate its prediction performance. The numerical results reveal that the NAR-GARCH model has satisfactory prediction results, especially for sharp upward or downward movements.
 摘要 iAbstract ii第一章 緒論 1第二章 文獻回顧 22.1自迴歸模型 22.2 GARCH模型 32.3向量自迴歸模型 52.4網絡向量自迴歸模型 62.5混合向量自迴歸模型 62.6長短期記憶模型 8第三章 研究方法與流程 93.1 AR模型 103.2 ARMA-GARCH-ST模型 103.3 VAR-GARCH模型 113.4 NAR-GARCH模型 123.5 mVAR-GARCH模型 153.6 LSTM模型 17第四章 實證研究 184.1評估指標 184.2投資報酬率 39第五章 結論 42參考文獻 44
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