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  本文選題：高頻數(shù)據(jù)　切入點：已實現(xiàn)波動率　出處：《大連理工大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：本文主要研究了我國股票市場高頻金融數(shù)據(jù)的波動率的預(yù)測問題。首先,本文介紹了高頻金融數(shù)據(jù),它是相對于以前的以每年、每月、每周等為頻率采集到的低頻金融數(shù)據(jù)而言的,通常指以每天、每小時、每分鐘甚至以每秒為頻率所采集到的按時間先后順序排列起來的金融數(shù)據(jù)序列。本文研究的數(shù)據(jù)樣本采用了上證綜指2010年1月4日到2012年6月29日的每1分鐘的高頻數(shù)據(jù)。 其次,本文利用己實現(xiàn)波動率來估計實際波動率,從理論上給出了已實現(xiàn)波動率的計算方法,并且給出了已實現(xiàn)波動率的極限性質(zhì),這是本文進(jìn)行研究的主要理論基礎(chǔ)。接下來本文提到了時間序列的一個重要性質(zhì)——長記憶性,并從時域和譜密度這兩個角度給出了3個關(guān)于長記憶性的定義,并且著重介紹了長記憶性的一種檢驗方法——R/S檢驗法。然后,本文提到了ARFIMA(p, d, q)模型,提出了進(jìn)行分?jǐn)?shù)階差分的意義,并且通過利用Stirling公式給出了一種做分?jǐn)?shù)階差分的簡單方法,通過簡單的R語言程序即可實現(xiàn)。 最后,本文通過對上述高頻金融數(shù)據(jù)的實證研究,對日對數(shù)己實現(xiàn)波動率(lnRV)的時間序列建立了ARFIMA(1,0.22,2)模型,并對其進(jìn)行了向后10步的預(yù)測,由預(yù)測結(jié)果可以知道本文所建立的模型是合適的。最后又通過分?jǐn)?shù)階差分和1階差分建模結(jié)果的比較可以知道本文提出的這種做分?jǐn)?shù)階差分的方法是有效且有意義的。
[Abstract]:This paper mainly studies the volatility prediction of high-frequency financial data in China's stock market. First, this paper introduces high-frequency financial data, which is compared with the previous annual, monthly, For low-frequency financial data collected at a frequency per week, usually in the form of a daily, an hour, A series of financial data in chronological order, even at frequencies per second, per minute. The data sample in this paper uses the high frequency data of every minute from January 4th 2010 to June 29th 2012 in the Shanghai Composite Index. Secondly, this paper estimates the actual volatility by using the realized volatility, gives the calculation method of the realized volatility theoretically, and gives the limit properties of the realized volatility. This is the main theoretical basis of this paper. In the next part of this paper, an important property of time series, long memory, is mentioned, and three definitions of long memory are given from the perspectives of time domain and spectral density. Then, the ARFIMAP, D, Q) model is mentioned, and the significance of fractional difference is put forward, and a simple method to do fractional order difference is given by using Stirling formula. Through a simple R language program can be achieved. Finally, based on the empirical study of the high frequency financial data mentioned above, this paper establishes the ARFIMA1 / 0.22 ~ 2) model for the time series of daily logarithmic self-realized volatility (LRV), and forecasts the model by 10 steps backward. From the prediction results, we can know that the model established in this paper is suitable. Finally, by comparing the results of fractional difference and first-order difference, we can see that the method proposed in this paper is effective and meaningful.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F832.51

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 徐梅,張世英,樊智;非平穩(wěn)和長記憶時間序列主頻率估計方法研究[J];天津大學(xué)學(xué)報;2003年04期

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本文編號：1559921