在金融領域，不確定的風險會帶來資產收益的波動，這是整個金融市場活躍的根本所在。股票市場往往是經濟發展的風向標，在股市中股票價格的變化往往受到各種資訊傳遞以及資本流動的影響。股價發生波動時，通常來講分為適度波動和劇烈波動兩種。在2015年中國大陸發生的股市震盪，先是初顯牛市，滬深兩市一路上揚，達到瘋牛，再隨後一路下挫，最終導致金融危機的爆發，這種股市的劇烈波動給投資者帶來巨大的損失，同時也給社會整體經濟造成嚴重的負面影響。
近年來，日內高頻交易數據可得性變高，為金融波動性的研究提供了新的手段。中國大陸金融市場具有明顯的異質性特徵，故本文運用HAR族模型來研究異質性對金融市場波動的影響，基於高頻數據對股指波動率進行預測的基礎模型，主要是HAR-RV模型,以往研究也有在考慮跳躍的基礎上將已實現波動RV進一步區分為跳躍波動JV和連續波動CV，將HAR-RV模型拓展為HAR-RV-J模型，本文引入長短期記憶網路（Long Short-Term Memory，LSTM），實證分析經過LSTM訓練後的HAR-RV-CJ模型預測能力的變化。
為了進一步評估模型的優劣，本文對上述三種模型進行了樣本外預測能力的評估。採用4種損失函數，通過基於滾動時間窗的SPA檢驗對各模型樣本外預測能力的優劣進行評估。實證分析表明：中國大陸滬深300指數已實現波動率具有明顯的記憶效應，過去的已實現波動率和未來一天的已實現波動率存在顯著的線性關係；已實現波動率的跳躍成分和連續成分也具有相似的特徵；引入LSTM後，日度和月度的已實現波動率及其對應的跳躍部分對未來波動率具有較強的解釋作用，在過去一周的解釋方面更加顯著；一般的HAR-RV模型具有一定的預測作用，特別是在波動相對平緩的時期。

關鍵字：HAR族模型；已實現波動率；LSTM；跳躍

In the financial field, uncertain risks will bring about fluctuations in asset returns, which is the root of the entire financial market. The stock market is often the vane of economic development, and changes in stock prices in the stock market are often affected by the transmission of various information and capital flows. When the stock price fluctuates, it is generally divided into two types: moderate fluctuation and severe fluctuation. In 2015, the stock market turmoil in mainland China first showed a bull market, the Shanghai and Shenzhen markets rose all the way, reached a mad bull, and then fell all the way, which eventually led to the outbreak of the financial crisis. This dramatic stock market volatility brought huge investors At the same time, it also has a serious negative impact on society’s overall economy.
In recent years, the availability of intra-day high-frequency data transaction data has become higher, providing a new means for the study of financial volatility. The Chinese mainland financial market has obvious heterogeneity characteristics, so this article uses the HAR family model to study the impact of heterogeneity on financial market volatility. The basic model for predicting stock index volatility based on high-frequency data is mainly the HAR-RV model. Previous research on the basis of considering the jump, the realized fluctuation RV is further divided into jump fluctuation JV and continuous fluctuation CV, and the HAR-RV model is extended to the HAR-RV-J model. This paper introduces a long short-term memory network (Long Short-Term Memory , LSTM), an empirical analysis of the changes in the prediction capabilities of the HAR-RV-CJ model after LSTM training.
In order to further evaluate the pros and cons of the model, this paper evaluates the out-of-sample prediction ability of the above three models. Four kinds of loss functions are used to evaluate the pros and cons of out-of-sample prediction ability of each model through SPA test based on rolling time window. Empirical analysis shows that the realized volatility of the CSI 300 Index in Mainland China has a significant memory effect. There is a significant linear relationship between the realized volatility in the past and the realized volatility in the next day; the jump component and continuous component of the realized volatility It also has similar characteristics; after the introduction of LSTM, the daily and monthly realized volatility and their corresponding jump parts have a strong explanatory effect on the future volatility, which is more significant in the interpretation of the past week; general HAR-RV The model has a certain predictive effect, especially during periods of relatively flat fluctuations.


Keywords: HAR family model; Realized volatility; LSTM; Jump

第一章 緒論 1
一、選題背景和選題意義 1
（一）選題背景 1
（二）選題意義 4
第二章 文獻綜述 6
一、波動率 6
二、已實現波動率 10
三、HAR模型 13
四、傳統預測方法與HAR模型的結合 15
第三章 模型與方法 18
一、HAR-RV模型 18
二、HAR-RV-CJ模型 20
三、SPA檢驗法 21
（一）波動率預測方法說明 21
（二）SPA檢驗方法說明 22
四、長短期記憶網路LSTM 24
第四章 實證分析 29
一、數據選擇 29
二、數據及訓練方法說明 29
三、最優採樣頻率 30
四、數據的描述性統計分析 33
五、引入跳躍的HAR-RV模型描述性統計分析 34
六、引入LSTM訓練HAR-RV模型的實證分析 38
第五章 模型評價與討論 41
一、模型評價方法 41
二、模型預測能力比較 42
三、SPA檢驗結果 44
第六章 總結與展望 46
參考文獻 50
致 謝 54

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