[1]AUDRINO F, SIGRIST F, BALLINARI D. The impact of sentiment and attention measures on stock market volatility[J/OL]. International Journal of Forecasting, 2020, 36(2): 334-357. DOI:10.1016/j.ijforecast.2019.05.010.

The impact of sentiment and attention measures on stock market volatility
情緒和注意力措施對(duì)股市波動(dòng)的影響

Francesco Audrino, Fabio Sigrist, Daniele Ballinari

Abstract
We analyze the impact of sentiment and attention variables on the stock market volatility by using a novel and extensive dataset that combines social media, news articles, information consumption, and search engine data. We apply a state-of-the-art sentiment classification technique in order to investigate the question of whether sentiment and attention measures contain additional predictive power for realized volatility when controlling for a wide range of economic and financial predictors. Using a penalized regression framework, we identify the most relevant variables to be investors’ attention, as measured by the number of Google searches on financial keywords (e.g. “financial market” and “stock market”), and the daily volume of company-specific short messages posted on StockTwits. In addition, our study shows that attention and sentiment variables are able to improve volatility forecasts significantly, although the magnitudes of the improvements are relatively small from an economic point of view.
我們通過(guò)使用結(jié)合了社交媒體、新聞文章坤邪、信息消費(fèi)和搜索引擎數(shù)據(jù)的新穎且廣泛的數(shù)據(jù)集來(lái)分析情緒和注意力變量對(duì)股市波動(dòng)的影響滥壕。 我們應(yīng)用最先進(jìn)的情緒分類技術(shù)來(lái)調(diào)查情緒和注意力測(cè)量在控制廣泛的經(jīng)濟(jì)和金融預(yù)測(cè)因素時(shí)是否包含對(duì)已實(shí)現(xiàn)波動(dòng)性的額外預(yù)測(cè)能力的問(wèn)題午笛。 使用懲罰回歸框架，我們通過(guò)金融關(guān)鍵詞（例如“金融市場(chǎng)”和“股票市場(chǎng)”）的谷歌搜索次數(shù)以及特定公司的每日交易量來(lái)衡量坦仍，確定了最受投資者關(guān)注的相關(guān)變量。 StockTwits 上發(fā)布的短消息熟丸。 此外症杏，我們的研究表明，注意力和情緒變量能夠顯著改善波動(dòng)性預(yù)測(cè)瑞信，盡管從經(jīng)濟(jì)角度來(lái)看改善的幅度相對(duì)較小厉颤。

[2]BHOWMIK R, WANG S. Stock Market Volatility and Return Analysis: A Systematic Literature Review[J/OL]. Entropy, 2020, 22(5): 522. DOI:10.3390/e22050522.

Stock Market Volatility and Return Analysis: A Systematic Literature Review
股市波動(dòng)與回報(bào)分析：系統(tǒng)文獻(xiàn)綜述

Roni Bhowmik
Shouyang Wang

Abstract
In the field of business research method, a literature review is more relevant than ever. Even though there has been lack of integrity and inflexibility in traditional literature reviews with questions being raised about the quality and trustworthiness of these types of reviews. This research provides a literature review using a systematic database to examine and cross-reference snowballing. In this paper, previous studies featuring a generalized autoregressive conditional heteroskedastic (GARCH) family-based model stock market return and volatility have also been reviewed. The stock market plays a pivotal role in today’s world economic activities, named a “barometer” and “alarm” for economic and financial activities in a country or region. In order to prevent uncertainty and risk in the stock market, it is particularly important to measure effectively the volatility of stock index returns. However, the main purpose of this review is to examine effective GARCH models recommended for performing market returns and volatilities analysis. The secondary purpose of this review study is to conduct a content analysis of return and volatility literature reviews over a period of 12 years (2008–2019) and in 50 different papers. The study found that there has been a significant change in research work within the past 10 years and most of researchers have worked for developing stock markets.
在商業(yè)研究方法領(lǐng)域，文獻(xiàn)綜述比以往任何時(shí)候都更加重要凡简。 盡管傳統(tǒng)的文獻(xiàn)評(píng)論缺乏完整性和靈活性逼友，人們對(duì)此類評(píng)論的質(zhì)量和可信度提出了質(zhì)疑。 這項(xiàng)研究提供了文獻(xiàn)綜述秤涩，使用系統(tǒng)數(shù)據(jù)庫(kù)來(lái)檢查和交叉引用滾雪球效應(yīng)帜乞。 在本文中，還回顧了之前基于廣義自回歸條件異方差（GARCH）家族模型股票市場(chǎng)回報(bào)和波動(dòng)性的研究筐眷。 股票市場(chǎng)在當(dāng)今世界經(jīng)濟(jì)活動(dòng)中發(fā)揮著舉足輕重的作用黎烈，被稱為一個(gè)國(guó)家或地區(qū)經(jīng)濟(jì)金融活動(dòng)的“晴雨表”和“警報(bào)器”。 為了防范股市的不確定性和風(fēng)險(xiǎn)匀谣，有效衡量股指收益的波動(dòng)性顯得尤為重要照棋。 然而，本次審查的主要目的是檢查推薦用于執(zhí)行市場(chǎng)回報(bào)和波動(dòng)率分析的有效 GARCH 模型武翎。 這項(xiàng)綜述研究的第二個(gè)目的是對(duì) 12 年（2008-2019 年）期間 50 篇不同論文中的回報(bào)和波動(dòng)性文獻(xiàn)綜述進(jìn)行內(nèi)容分析烈炭。 研究發(fā)現(xiàn)，過(guò)去10年里研究工作發(fā)生了重大變化宝恶，大多數(shù)研究人員都致力于發(fā)展股票市場(chǎng)符隙。

Keywords:
stock returns; volatility; GARCH family model; complexity in market volatility forecasting

1. Introduction
   In the context of economic globalization, especially after the impact of the contemporary international financial crisis, the stock market has experienced unprecedented fluctuations. This volatility increases the uncertainty and risk of the stock market and is detrimental to the normal operation of the stock market. To reduce this uncertainty, it is particularly important to measure accurately the volatility of stock index returns. At the same time, due to the important position of the stock market in the global economy, the beneficial development of the stock market has become the focus. Therefore, the knowledge of theoretical and literature significance of volatility are needed to measure the volatility of stock index returns.
   在經(jīng)濟(jì)全球化背景下，特別是當(dāng)代國(guó)際金融危機(jī)沖擊后垫毙，股市出現(xiàn)了前所未有的波動(dòng)霹疫。 這種波動(dòng)增加了股市的不確定性和風(fēng)險(xiǎn)，不利于股市的正常運(yùn)行综芥。 為了減少這種不確定性更米，準(zhǔn)確衡量股指收益的波動(dòng)性尤為重要。 同時(shí)毫痕，由于股票市場(chǎng)在全球經(jīng)濟(jì)中的重要地位征峦，股票市場(chǎng)的良性發(fā)展成為人們關(guān)注的焦點(diǎn)。 因此消请，需要了解波動(dòng)性的理論和文獻(xiàn)意義來(lái)衡量股指收益的波動(dòng)性栏笆。

Volatility is a hot issue in economic and financial research. Volatility is one of the most important characteristics of financial markets. It is directly related to market uncertainty and affects the investment behavior of enterprises and individuals. A study of the volatility of financial asset returns is also one of the core issues in modern financial research and this volatility is often described and measured by the variance of the rate of return. However, forecasting perfect market volatility is difficult work and despite the availability of various models and techniques, not all of them work equally for all stock markets. It is for this reason that researchers and financial analysts face such a complexity in market returns and volatilities forecasting.
波動(dòng)性是經(jīng)濟(jì)和金融研究的熱點(diǎn)問(wèn)題。 波動(dòng)性是金融市場(chǎng)最重要的特征之一臊泰。 它與市場(chǎng)的不確定性直接相關(guān)蛉加，影響企業(yè)和個(gè)人的投資行為。 對(duì)金融資產(chǎn)收益率波動(dòng)性的研究也是現(xiàn)代金融研究的核心問(wèn)題之一，這種波動(dòng)性往往用收益率的方差來(lái)描述和衡量针饥。 然而厂抽，預(yù)測(cè)完美的市場(chǎng)波動(dòng)性是一項(xiàng)艱巨的工作，盡管有各種模型和技術(shù)可供使用丁眼，但并非所有模型和技術(shù)都同樣適用于所有股票市場(chǎng)筷凤。 正是由于這個(gè)原因，研究人員和金融分析師在市場(chǎng)回報(bào)和波動(dòng)性預(yù)測(cè)方面面臨著如此復(fù)雜的問(wèn)題苞七。

The traditional econometric model often assumes that the variance is constant, that is, the variance is kept constant at different times. An accurate measurement of the rate of return’s fluctuation is directly related to the correctness of portfolio selection, the effectiveness of risk management, and the rationality of asset pricing. However, with the development of financial theory and the deepening of empirical research, it was found that this assumption is not reasonable. Additionally, the volatility of asset prices is one of the most puzzling phenomena in financial economics. It is a great challenge for investors to get a pure understanding of volatility.
傳統(tǒng)的計(jì)量經(jīng)濟(jì)學(xué)模型往往假設(shè)方差是恒定的藐守，即方差在不同時(shí)刻保持恒定。 收益率波動(dòng)的準(zhǔn)確計(jì)量直接關(guān)系到投資組合選擇的正確性蹂风、風(fēng)險(xiǎn)管理的有效性以及資產(chǎn)定價(jià)的合理性卢厂。 然而，隨著金融理論的發(fā)展和實(shí)證研究的深入惠啄，人們發(fā)現(xiàn)這種假設(shè)并不合理慎恒。 此外，資產(chǎn)價(jià)格的波動(dòng)是金融經(jīng)濟(jì)學(xué)中最令人費(fèi)解的現(xiàn)象之一撵渡。 對(duì)于投資者來(lái)說(shuō)巧号，獲得對(duì)波動(dòng)性的純粹理解是一個(gè)巨大的挑戰(zhàn)。

A literature reviews act as a significant part of all kinds of research work. Literature reviews serve as a foundation for knowledge progress, make guidelines for plan and practice, provide grounds of an effect, and, if well guided, have the capacity to create new ideas and directions for a particular area [1]. Similarly, they carry out as the basis for future research and theory work. This paper conducts a literature review of stock returns and volatility analysis based on generalized autoregressive conditional heteroskedastic (GARCH) family models. Volatility refers to the degree of dispersion of random variables.
文獻(xiàn)綜述是各類研究工作的重要組成部分姥闭。 文獻(xiàn)綜述可以作為知識(shí)進(jìn)步的基礎(chǔ)丹鸿，為計(jì)劃和實(shí)踐提供指導(dǎo)，提供效果的基礎(chǔ)棚品，并且如果指導(dǎo)得當(dāng)靠欢，有能力為特定領(lǐng)域創(chuàng)造新的想法和方向[1]。 同樣铜跑，它們也是未來(lái)研究和理論工作的基礎(chǔ)门怪。 本文對(duì)基于廣義自回歸條件異方差（GARCH）族模型的股票收益和波動(dòng)率分析進(jìn)行了文獻(xiàn)綜述。 波動(dòng)性是指隨機(jī)變量的分散程度锅纺。

Financial market volatility is mainly reflected in the deviation of the expected future value of assets. The possibility, that is, volatility, represents the uncertainty of the future price of an asset. This uncertainty is usually characterized by variance or standard deviation. There are currently two main explanations in the academic world for the relationship between these two: The leverage effect and the volatility feedback hypothesis. Leverage often means that unfavorable news appears, stock price falls, leading to an increase in the leverage factor, and thus the degree of stock volatility increases. Conversely, the degree of volatility weakens; volatility feedback can be simply described as unpredictable stock volatility that will inevitably lead to higher risk in the future.
金融市場(chǎng)的波動(dòng)主要體現(xiàn)在資產(chǎn)預(yù)期未來(lái)價(jià)值的偏差掷空。 可能性，即波動(dòng)性囤锉，代表了資產(chǎn)未來(lái)價(jià)格的不確定性坦弟。 這種不確定性通常用方差或標(biāo)準(zhǔn)差來(lái)表征。 目前學(xué)術(shù)界對(duì)于兩者之間的關(guān)系主要有兩種解釋：杠桿效應(yīng)和波動(dòng)反饋假說(shuō)官地。 杠桿往往意味著不利消息出現(xiàn)酿傍，股價(jià)下跌，導(dǎo)致杠桿系數(shù)增大驱入，從而股票波動(dòng)程度加大赤炒。 反之氯析，波動(dòng)程度減弱； 波動(dòng)反饋可以簡(jiǎn)單地描述為不可預(yù)測(cè)的股票波動(dòng)莺褒，這將不可避免地導(dǎo)致未來(lái)更高的風(fēng)險(xiǎn)掩缓。

There are many factors that affect price movements in the stock market. Firstly, there is the impact of monetary policy on the stock market, which is extremely substantial. If a loose monetary policy is implemented in a year, the probability of a stock market index rise will increase. On the other hand, if a relatively tight monetary policy is implemented in a year, the probability of a stock market index decline will increase. Secondly, there is the impact of interest rate liberalization on risk-free interest rates. Looking at the major global capital markets, the change in risk-free interest rates has a greater correlation with the current stock market. In general, when interest rates continue to rise, the risk-free interest rate will rise, and the cost of capital invested in the stock market will rise simultaneously. As a result, the economy is expected to gradually pick up during the release of the reform dividend, and the stock market is expected to achieve a higher return on investment.
影響股票市場(chǎng)價(jià)格變動(dòng)的因素有很多。 首先是貨幣政策對(duì)股市的影響非常大遵岩。 如果一年內(nèi)實(shí)行寬松的貨幣政策你辣，股市指數(shù)上漲的概率就會(huì)增加。 另一方面旷余，如果一年內(nèi)實(shí)施相對(duì)從緊的貨幣政策，股市指數(shù)下跌的概率就會(huì)增加扁达。 其次正卧，利率市場(chǎng)化對(duì)無(wú)風(fēng)險(xiǎn)利率的影響。 縱觀全球主要資本市場(chǎng)跪解，無(wú)風(fēng)險(xiǎn)利率的變化與當(dāng)前股市有較大的相關(guān)性炉旷。 一般來(lái)說(shuō)，當(dāng)利率持續(xù)上升時(shí)叉讥，無(wú)風(fēng)險(xiǎn)利率就會(huì)上升窘行，投資于股市的資金成本也會(huì)同步上升。 因此图仓，經(jīng)濟(jì)有望在改革紅利釋放期間逐步回暖罐盔，股市有望獲得較高的投資回報(bào)。

Volatility is the tendency for prices to change unexpectedly [2], however, all kinds of volatility is not bad. At the same time, financial market volatility has also a direct impact on macroeconomic and financial stability. Important economic risk factors are generally highly valued by governments around the world. Therefore, research on the volatility of financial markets has always been the focus of financial economists and financial practitioners. Nowadays, a large part of the literature has studied some characteristics of the stock market, such as the leverage effect of volatility, the short-term memory of volatility, and the GARCH effect, etc., but some researchers show that when adopting short-term memory by the GARCH model, there is usually a confusing phenomenon, as the sampling interval tends to zero. The characterization of the tail of the yield generally assumes an ideal situation, that is, obeys the normal distribution, but this perfect situation is usually not established.
波動(dòng)性是價(jià)格發(fā)生意外變化的趨勢(shì)[2]救崔，但是惶看，各種波動(dòng)性都還不錯(cuò)。 同時(shí)六孵，金融市場(chǎng)波動(dòng)也直接影響宏觀經(jīng)濟(jì)和金融穩(wěn)定纬黎。 重要的經(jīng)濟(jì)風(fēng)險(xiǎn)因素普遍受到世界各國(guó)政府的高度重視。 因此劫窒，對(duì)金融市場(chǎng)波動(dòng)性的研究一直是金融經(jīng)濟(jì)學(xué)家和金融從業(yè)者關(guān)注的焦點(diǎn)本今。 如今，很大一部分文獻(xiàn)研究了股票市場(chǎng)的一些特征主巍，例如波動(dòng)性的杠桿效應(yīng)冠息、波動(dòng)性的短期記憶以及GARCH效應(yīng)等，但也有研究者表明孕索，當(dāng)采用短期 GARCH模型的術(shù)語(yǔ)記憶通常存在一個(gè)令人困惑的現(xiàn)象铐达，即采樣間隔趨于零。 收益率尾部的表征一般假設(shè)一種理想情況檬果，即服從正態(tài)分布瓮孙，但這種完美情況通常不成立唐断。

Researchers have proposed different distributed models in order to better describe the thick tail of the daily rate of return. Engle [3] first proposed an autoregressive conditional heteroscedasticity model (ARCH model) to characterize some possible correlations of the conditional variance of the prediction error. Bollerslev [4] has been extended it to form a generalized autoregressive conditional heteroskedastic model (GARCH model). Later, the GARCH model rapidly expanded and a GARCH family model was created.
研究人員提出了不同的分布式模型，以便更好地描述日收益率的粗尾杭抠。 Engle[3]首先提出了自回歸條件異方差模型（ARCH模型）來(lái)表征預(yù)測(cè)誤差的條件方差的一些可能的相關(guān)性脸甘。 Bollerslev [4] 對(duì)其進(jìn)行了擴(kuò)展，形成了廣義自回歸條件異方差模型（GARCH 模型）偏灿。 后來(lái)GARCH模型迅速擴(kuò)展丹诀，創(chuàng)建了GARCH家族模型。

When employing GARCH family models to analyze and forecast return volatility, selection of input variables for forecasting is crucial as the appropriate and essential condition will be given for the method to have a stationary solution and perfect matching [5]. It has been shown in several findings that the unchanged model can produce suggestively different results when it is consumed with different inputs. Thus, another key purpose of this literature review is to observe studies which use directional prediction accuracy model as a yardstick from a realistic point of understanding and has the core objective of the forecast of financial time series in stock market return. Researchers estimate little forecast error, namely measured as mean absolute deviation (MAD), root mean squared error (RMSE), mean absolute error (MAE), and mean squared error (MSE) which do not essentially interpret into capital gain [6,7]. Some others mention that the predictions are not required to be precise in terms of NMSE (normalized mean squared error) [8]. It means that finding the low rate of root mean squared error does not feed high returns, in another words, the relationship is not linear between two.
當(dāng)采用GARCH族模型分析和預(yù)測(cè)收益波動(dòng)性時(shí)翁垂，預(yù)測(cè)輸入變量的選擇至關(guān)重要铆遭，因?yàn)檫@將給出該方法具有平穩(wěn)解和完美匹配的適當(dāng)且必要的條件[5]。 多項(xiàng)研究結(jié)果表明沿猜，當(dāng)使用不同的輸入時(shí)枚荣，未更改的模型可能會(huì)產(chǎn)生明顯不同的結(jié)果。 因此啼肩，本文綜述的另一個(gè)重要目的是從現(xiàn)實(shí)的理解角度觀察以方向性預(yù)測(cè)精度模型為尺度橄妆、以股市收益中的金融時(shí)間序列預(yù)測(cè)為核心目標(biāo)的研究。 研究人員估計(jì)預(yù)測(cè)誤差很小祈坠，即以平均絕對(duì)偏差 (MAD)害碾、均方根誤差 (RMSE)、平均絕對(duì)誤差 (MAE) 和均方誤差 (MSE) 來(lái)衡量赦拘，這些誤差本質(zhì)上并不解釋為資本收益 [6,7 ]慌随。 其他一些人提到預(yù)測(cè)不需要在 NMSE（歸一化均方誤差）方面精確 [8]。 這意味著找到低均方根誤差率并不能帶來(lái)高回報(bào)躺同，換句話說(shuō)儒陨，兩者之間的關(guān)系不是線性的。

In this manuscript, it is proposed to categorize the studies not only by their model selection standards but also for the inputs used for the return volatility as well as how precise it is spending them in terms of return directions. In this investigation, the authors repute studies which use percentage of success trades benchmark procedures for analyzing the researchers’ proposed models. From this theme, this study’s authentic approach is compared with earlier models in the literature review for input variables used for forecasting volatility and how precise they are in analyzing the direction of the related time series. There are other review studies on return and volatility analysis and GARCH-family based financial forecasting methods done by a number of researchers [9,10,11,12,13]. Consequently, the aim of this manuscript is to put forward the importance of sufficient and necessary conditions for model selection and contribute for the better understanding of academic researchers and financial practitioners.
在這份手稿中笋籽，建議不僅根據(jù)模型選擇標(biāo)準(zhǔn)對(duì)研究進(jìn)行分類蹦漠，而且還根據(jù)用于回報(bào)波動(dòng)性的輸入以及在回報(bào)方向方面花費(fèi)它們的精確程度對(duì)研究進(jìn)行分類。 在這項(xiàng)調(diào)查中车海，作者贊揚(yáng)了使用成功百分比交易基準(zhǔn)程序來(lái)分析研究人員提出的模型的研究笛园。 從這個(gè)主題出發(fā)，本研究的真實(shí)方法與文獻(xiàn)綜述中用于預(yù)測(cè)波動(dòng)性的輸入變量的早期模型以及它們?cè)诜治鱿嚓P(guān)時(shí)間序列的方向時(shí)的精確度進(jìn)行了比較侍芝。 還有許多研究人員對(duì)回報(bào)和波動(dòng)性分析以及基于 GARCH 系列的財(cái)務(wù)預(yù)測(cè)方法進(jìn)行的其他綜述研究 [9,10,11,12,13]研铆。 因此，本文的目的是提出模型選擇充分必要條件的重要性州叠，并有助于學(xué)術(shù)研究人員和金融從業(yè)者更好地理解棵红。

Systematic reviews have most notable been expanded by medical science as a way to synthesize research recognition in a systematic, transparent, and reproducible process. Despite the opportunity of this technique, its exercise has not been overly widespread in business research, but it is expanding day by day. In this paper, the authors have used the systematic review process because the target of a systematic review is to determine all empirical indication that fits the pre-decided inclusion criteria or standard of response to a certain research question. Researchers proved that GARCH is the most suitable model to use when one has to analysis the volatility of the returns of stocks with big volumes of observations [3,4,6,9,13]. Researchers observe keenly all the selected literature to answer the following research question: What are the effective GARCH models to recommend for performing market volatility and return analysis?
醫(yī)學(xué)科學(xué)最顯著地?cái)U(kuò)展了系統(tǒng)評(píng)價(jià)，作為在系統(tǒng)咧栗、透明和可重復(fù)的過(guò)程中綜合研究認(rèn)可的一種方式逆甜。 盡管有這種技術(shù)的機(jī)會(huì)虱肄，但它的運(yùn)用在商業(yè)研究中并沒(méi)有過(guò)于廣泛，但它正在日益擴(kuò)大交煞。 在本文中咏窿，作者使用了系統(tǒng)評(píng)價(jià)過(guò)程，因?yàn)橄到y(tǒng)評(píng)價(jià)的目標(biāo)是確定符合預(yù)先確定的納入標(biāo)準(zhǔn)或?qū)δ硞€(gè)研究問(wèn)題的回答標(biāo)準(zhǔn)的所有經(jīng)驗(yàn)指標(biāo)素征。 研究人員證明集嵌，當(dāng)需要通過(guò)大量觀察來(lái)分析股票回報(bào)的波動(dòng)性時(shí)，GARCH 是最合適的模型 [3,4,6,9,13]御毅。 研究人員敏銳地觀察了所有選定的文獻(xiàn)根欧，以回答以下研究問(wèn)題：推薦哪些有效的 GARCH 模型來(lái)進(jìn)行市場(chǎng)波動(dòng)和回報(bào)分析？

The main contribution of this paper is found in the following four aspects: (1) The best GARCH models can be recommended for stock market returns and volatilities evaluation. (2) The manuscript considers recent papers, 2008 to 2019, which have not been covered in previous studies. (3) In this study, both qualitative and quantitative processes have been used to examine the literature involving stock returns and volatilities. (4) The manuscript provides a study based on journals that will help academics and researchers recognize important journals that they can denote for a literature review, recognize factors motivating analysis stock returns and volatilities, and can publish their worth study manuscripts.
本文的主要貢獻(xiàn)體現(xiàn)在以下四個(gè)方面：（1）可以推薦最好的GARCH模型用于股票市場(chǎng)收益和波動(dòng)性評(píng)估端蛆。 (2) 本文考慮了 2008 年至 2019 年最近的論文凤粗，這些論文在之前的研究中尚未涵蓋。 (3) 在本研究中欺税，使用定性和定量方法來(lái)檢驗(yàn)涉及股票收益和波動(dòng)性的文獻(xiàn)侈沪。 (4) 手稿提供了基于期刊的研究揭璃，這將幫助學(xué)者和研究人員認(rèn)識(shí)到他們可以表示進(jìn)行文獻(xiàn)綜述的重要期刊晚凿，認(rèn)識(shí)到激勵(lì)分析股票收益和波動(dòng)性的因素，并可以發(fā)表他們值得研究的手稿瘦馍。

Realized volatility forecast: structural breaks, long memory, asymmetry, and day-of-the-week effect
已實(shí)現(xiàn)的波動(dòng)率預(yù)測(cè)：結(jié)構(gòu)性斷裂歼秽、長(zhǎng)記憶、不對(duì)稱性和星期效應(yīng)
楊科; 陳浪南
Ke Yang, Langnan Chen

Abstract
We investigate the properties of the realized volatility in Chinese stock markets by employing the high-frequency data of Shanghai Stock Exchange Composite Index and four individual stocks from Shanghai Stock Exchange and Shenzhen Stock Exchange, and find that the volatility exhibits the properties of long-term memory, structural breaks, asymmetry, and day-of-the-week effect. In addition, the structural breaks only partially explain the long memory. To capture these properties simultaneously, we derive an adaptive asymmetry heterogeneous autoregressive model with day-of-the-week effect and fractionally integrated generalized autoregressive conditional heteroskedasticity errors (HAR-D-FIGARCH) and use it to conduct a forecast of realized volatility. Compared with other heterogeneous autoregressive realized volatility models, the proposed model improves the in-sample fit significantly. The proposed model is the best model for the day-ahead realized volatility forecasts among the six models based on various loss functions by utilizing the superior predictive ability test.
我們利用上證綜指以及滬深交易所四只個(gè)股的高頻數(shù)據(jù)考察了中國(guó)股票市場(chǎng)的實(shí)際波動(dòng)率的性質(zhì)情组，發(fā)現(xiàn)波動(dòng)率呈現(xiàn)出長(zhǎng)期波動(dòng)的性質(zhì)燥筷。 記憶、結(jié)構(gòu)斷裂院崇、不對(duì)稱和星期效應(yīng)肆氓。 此外，結(jié)構(gòu)斷裂只能部分解釋長(zhǎng)記憶底瓣。 為了同時(shí)捕獲這些屬性谢揪，我們推導(dǎo)了具有星期效應(yīng)和分?jǐn)?shù)積分廣義自回歸條件異方差誤差（HAR-D-FIGARCH）的自適應(yīng)不對(duì)稱異質(zhì)自回歸模型，并用它來(lái)預(yù)測(cè)已實(shí)現(xiàn)的波動(dòng)率捐凭。 與其他異構(gòu)自回歸實(shí)現(xiàn)波動(dòng)率模型相比拨扶，該模型顯著改善了樣本內(nèi)擬合。 通過(guò)利用優(yōu)越的預(yù)測(cè)能力測(cè)試茁肠，所提出的模型是基于各種損失函數(shù)的六種模型中日前實(shí)現(xiàn)波動(dòng)率預(yù)測(cè)的最佳模型患民。

Realized Volatility Forecast of Stock Index Under Structural Breaks
結(jié)構(gòu)性突破下股指波動(dòng)率預(yù)測(cè)實(shí)現(xiàn)

Ke Yang, Langnan Chen, Fengping Tian

We investigate the realized volatility forecast of stock indices under the structural breaks. We utilize a pure multiple mean break model to identify the possibility of structural breaks in the daily realized volatility series by employing the intraday high-frequency data of the Shanghai Stock Exchange Composite Index and the five sectoral stock indices in Chinese stock markets for the period 4 January 2000 to 30 December 2011. We then conduct both in-sample tests and out-of-sample forecasts to examine the effects of structural breaks on the performance of ARFIMAX-FIGARCH models for the realized volatility forecast by utilizing a variety of estimation window sizes designed to accommodate potential structural breaks. The results of the in-sample tests show that there are multiple breaks in all realized volatility series. The results of the out-of-sample point forecasts indicate that the combination forecasts with time-varying weights across individual forecast models estimated with different estimation windows perform well. In particular, nonlinear combination forecasts with the weights chosen based on a non-parametric kernel regression and linear combination forecasts with the weights chosen based on the non-negative restricted least squares and Schwarz information criterion appear to be the most accurate methods in point forecasting for realized volatility under structural breaks. We also conduct an interval forecast of the realized volatility for the combination approaches, and find that the interval forecast for nonlinear combination approaches with the weights chosen according to a non-parametric kernel regression performs best among the competing models. Copyright ? 2014 John Wiley & Sons, Ltd.
我們研究了結(jié)構(gòu)性突破下股指的已實(shí)現(xiàn)波動(dòng)率預(yù)測(cè)。 我們利用純多重均值突破模型垦梆，利用上證綜指和中國(guó)股市五個(gè)板塊股指第 4 階段的日內(nèi)高頻數(shù)據(jù)匹颤，來(lái)識(shí)別日實(shí)現(xiàn)波動(dòng)率序列出現(xiàn)結(jié)構(gòu)性突破的可能性仅孩。 2000 年 1 月至 2011 年 12 月 30 日。然后惋嚎，我們進(jìn)行樣本內(nèi)測(cè)試和樣本外預(yù)測(cè)杠氢，以檢查結(jié)構(gòu)性斷裂對(duì) ARFIMAX-FIGARCH 模型性能的影響，以利用各種估計(jì)窗口大小進(jìn)行實(shí)際波動(dòng)率預(yù)測(cè) 旨在適應(yīng)潛在的結(jié)構(gòu)斷裂另伍。 樣本內(nèi)檢驗(yàn)的結(jié)果表明鼻百，所有已實(shí)現(xiàn)的波動(dòng)率序列均存在多次突破。 樣本外點(diǎn)預(yù)測(cè)的結(jié)果表明摆尝，使用不同估計(jì)窗口估計(jì)的各個(gè)預(yù)測(cè)模型的時(shí)變權(quán)重組合預(yù)測(cè)表現(xiàn)良好温艇。 特別是，基于非參數(shù)核回歸選擇權(quán)重的非線性組合預(yù)測(cè)和基于非負(fù)限制最小二乘和 Schwarz 信息準(zhǔn)則選擇權(quán)重的線性組合預(yù)測(cè)似乎是點(diǎn)預(yù)測(cè)中最準(zhǔn)確的方法堕汞。 結(jié)構(gòu)性斷裂下的實(shí)際波動(dòng)勺爱。 我們還對(duì)組合方法的已實(shí)現(xiàn)波動(dòng)率進(jìn)行了區(qū)間預(yù)測(cè)，并發(fā)現(xiàn)根據(jù)非參數(shù)核回歸選擇權(quán)重的非線性組合方法的區(qū)間預(yù)測(cè)在競(jìng)爭(zhēng)模型中表現(xiàn)最佳讯检。 版權(quán)所有 ? 2014 約翰·威利父子有限公司