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1

Asai, Manabu, and Michael McAleer. "Asymmetric Multivariate Stochastic Volatility." Econometric Reviews 25, no. 2-3 (September 2006): 453–73. http://dx.doi.org/10.1080/07474930600712913.

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2

Hoti, Suhejla, Michael McAleer, and Laurent L. Pauwels. "Multivariate volatility in environmental finance." Mathematics and Computers in Simulation 78, no. 2-3 (July 2008): 189–99. http://dx.doi.org/10.1016/j.matcom.2008.01.038.

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3

Maasoumi, Esfandiar, and Michael McAleer. "Multivariate Stochastic Volatility: An Overview." Econometric Reviews 25, no. 2-3 (September 2006): 139–44. http://dx.doi.org/10.1080/07474930600712806.

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4

Asai, Manabu, Michael McAleer, and Jun Yu. "Multivariate Stochastic Volatility: A Review." Econometric Reviews 25, no. 2-3 (September 2006): 145–75. http://dx.doi.org/10.1080/07474930600713564.

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5

Caporin, Massimiliano, and Paolo Paruolo. "Proximity-Structured Multivariate Volatility Models." Econometric Reviews 34, no. 5 (November 10, 2014): 559–93. http://dx.doi.org/10.1080/07474938.2013.807102.

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6

Dovonon, Prosper, Sílvia Gonçalves, and Nour Meddahi. "Bootstrapping realized multivariate volatility measures." Journal of Econometrics 172, no. 1 (January 2013): 49–65. http://dx.doi.org/10.1016/j.jeconom.2012.08.003.

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7

Bensafta, Kamel Malik, and Gervasio Semedo. "De la transmission de la volatilité à la contagion entre marchés boursiers : l’éclairage d’un modèle VAR non linéaire avec bris structurels en variance." Articles 85, no. 1 (May 18, 2010): 13–76. http://dx.doi.org/10.7202/039734ar.

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Résumé Nous développons dans cet article une modélisation vectorielle autorégressive non linéaire pour l’étude des interdépendances entre les marchés boursiers. Parmi les innovations de ce travail, nous introduisons un bris structurel dans la matrice des variances-covariances conditionnelle d’un processus GARCH multivarié. Dans cet ordre d’idée, nous considérons une spécification BEKK de cette matrice augmentée avec des régresseurs de transmission des chocs de volatilité entre les marchés. L’objectif de cette modification est de répondre à plusieurs biais importants dans la mesure des volatilités et des corrélations entre les marchés : d’une part, le biais de surestimation de la persistance des chocs de volatilité; d’autre part, les biais d’hétéroscédasticité et de variables omises dans la mesure des corrélations. Nous considérons ici un échantillon de 11 marchés boursiers d’Europe, d’Amérique du Nord et d’Asie avec des données hebdomadaires des indices les plus larges entre 1985 et 2006. Plusieurs résultats intéressants sont obtenus avec cette modélisation : la réduction de la persistance des chocs de volatilité; l’évidence d’une transmission des prix et des incertitudes du marché américain vers les marchés européens et asiatiques; l’existence de phénomène de transmission régionale en Europe et en Asie; mis à part le krach américain d’octobre 1987, toutes les crises ne sont pas systématiquement contagieuses. Au final, il n’est pas évident que la libéralisation financière isole les marchés des crises financières diverses, bien que l’intégration soit un vecteur d’efficience des marchés. Les crises et le phénomène de contagion en période de crise peuvent être considérés comme des processus de rééquilibrage des marchés qui doivent être encadrés, régulés et supervisés.
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8

Vo, Minh. "Oil and stock market volatility: A multivariate stochastic volatility perspective." Energy Economics 33, no. 5 (September 2011): 956–65. http://dx.doi.org/10.1016/j.eneco.2011.03.005.

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9

Haug, Stephan, and Robert Stelzer. "MULTIVARIATE ECOGARCH PROCESSES." Econometric Theory 27, no. 2 (September 13, 2010): 344–71. http://dx.doi.org/10.1017/s0266466610000289.

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A multivariate extension of the exponential continuous time GARCH (p, q) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated, and ways to model a component-wise leverage effect are presented.
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10

So, Mike K. P., and C. Y. Choi. "A multivariate threshold stochastic volatility model." Mathematics and Computers in Simulation 79, no. 3 (December 2008): 306–17. http://dx.doi.org/10.1016/j.matcom.2007.12.003.

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11

Brechmann, E. C., M. Heiden, and Y. Okhrin. "A multivariate volatility vine copula model." Econometric Reviews 37, no. 4 (April 2, 2016): 281–308. http://dx.doi.org/10.1080/07474938.2015.1096695.

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12

Barndorff-Nielsen, Ole Eiler, and Robert Stelzer. "THE MULTIVARIATE supOU STOCHASTIC VOLATILITY MODEL." Mathematical Finance 23, no. 2 (July 6, 2011): 275–96. http://dx.doi.org/10.1111/j.1467-9965.2011.00494.x.

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13

Philipov, Alexander, and Mark E. Glickman. "Multivariate Stochastic Volatility via Wishart Processes." Journal of Business & Economic Statistics 24, no. 3 (July 2006): 313–28. http://dx.doi.org/10.1198/073500105000000306.

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14

Garcia, R., E. Ghysels, E. Renault, and P. Rodrigues. "Special Issue on "Multivariate Volatility Models"." Journal of Financial Econometrics 7, no. 4 (September 21, 2009): 339–40. http://dx.doi.org/10.1093/jjfinec/nbp017.

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15

Bollerslev, Tim, Nour Meddahi, and Serge Nyawa. "High-dimensional multivariate realized volatility estimation." Journal of Econometrics 212, no. 1 (September 2019): 116–36. http://dx.doi.org/10.1016/j.jeconom.2019.04.023.

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16

Cotter, John, and Simon Stevenson. "Multivariate Modeling of Daily REIT Volatility." Journal of Real Estate Finance and Economics 32, no. 3 (March 29, 2006): 305–25. http://dx.doi.org/10.1007/s11146-006-6804-9.

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17

Bauer, Gregory H., and Keith Vorkink. "Forecasting multivariate realized stock market volatility." Journal of Econometrics 160, no. 1 (January 2011): 93–101. http://dx.doi.org/10.1016/j.jeconom.2010.03.021.

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18

Chiriac, Roxana, and Valeri Voev. "Modelling and forecasting multivariate realized volatility." Journal of Applied Econometrics 26, no. 6 (February 1, 2010): 922–47. http://dx.doi.org/10.1002/jae.1152.

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19

Bauwens, Luc, Christian M. Hafner, and Diane Pierret. "MULTIVARIATE VOLATILITY MODELING OF ELECTRICITY FUTURES." Journal of Applied Econometrics 28, no. 5 (May 18, 2012): 743–61. http://dx.doi.org/10.1002/jae.2280.

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20

Asai, Manabu, and Michael McAleer. "Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes." International Journal of Statistics and Probability 6, no. 6 (September 15, 2017): 13. http://dx.doi.org/10.5539/ijsp.v6n6p13.

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The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.
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21

Bouchareb, Saoussan, Mohamed Salah Chiadmi, and Fouzia Ghaiti. "Modeling Mediterranean Stock Markets Volatility with Univariate and Multivariate Approaches." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 16 (August 4, 2021): 457–68. http://dx.doi.org/10.37394/23203.2021.16.41.

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In our study we use the univariate and multivariate GARCH models to analyze the volatility behavior of the daily data of four Mediterranean stock markets (Morocco, Turkey, Spain, and France) spanning the period 2000-2020. We find a strong evidence of persisting of volatility in each of these markets. Results also indicate that both the univariate and the multivariate approaches capture well the ARCH and GARCH effects. We analyze the conditional covariances, and co-volatility spillovers between the Moroccan stock market and the three other Mediterranean stock markets. In order to study co-volatility spillovers, our work is built on the diagonal BEKK model especially the conditional covariances.
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22

Li, Yong, Fang-Ping Peng, and Hao-Feng Xu. "Bayesian Testing for Asset Volatility Persistence on Multivariate Stochastic Volatility Models." Journal of Mathematical Finance 02, no. 01 (2012): 83–89. http://dx.doi.org/10.4236/jmf.2012.21010.

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23

Metsileng, Lebotsa Daniel, Ntebogang Dinah Moroke, and Johannes Tshepiso Tsoku. "The Application of the Multivariate GARCH Models on the BRICS Exchange Rates." Academic Journal of Interdisciplinary Studies 9, no. 4 (July 10, 2020): 23. http://dx.doi.org/10.36941/ajis-2020-0058.

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The study investigated the BRICS exchange rate volatility using the Multivariate GARCH models. The study used the monthly time series data for the period January 2008 to January 2018. The BEKK-GARCH model revealed that all the variables were found to be statistically significant. The diagonal parameters estimates showed that only Russia and South Africa were statistically significant. This implied that the conditional variance of Russia and South Africa’s exchange rates are affected by their own past conditional volatility and other BRICS exchange rates past conditional volatility. The BEKK-GARCH model also revealed that there is a bidirectional volatility transmission between Russia and South Africa. The results from the DCC-GARCH model revealed that Brazil, China, Russia and South Africa had the highest volatility persistence and India has the least volatility persistence. All the BRICS exchange rates show that the fitted residuals are not normally distributed except for Russia. The recommendations for future studies were articulated.
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24

Candila, Vincenzo. "Multivariate Analysis of Cryptocurrencies." Econometrics 9, no. 3 (July 1, 2021): 28. http://dx.doi.org/10.3390/econometrics9030028.

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Recently, the world of cryptocurrencies has experienced an undoubted increase in interest. Since the first cryptocurrency appeared in 2009 in the aftermath of the Great Recession, the popularity of digital currencies has, year by year, risen continuously. As of February 2021, there are more than 8525 cryptocurrencies with a market value of approximately USD 1676 billion. These particular assets can be used to diversify the portfolio as well as for speculative actions. For this reason, investigating the daily volatility and co-volatility of cryptocurrencies is crucial for investors and portfolio managers. In this work, the interdependencies among a panel of the most traded digital currencies are explored and evaluated from statistical and economic points of view. Taking advantage of the monthly Google queries (which appear to be the factors driving the price dynamics) on cryptocurrencies, we adopted a mixed-frequency approach within the Dynamic Conditional Correlation (DCC) model. In particular, we introduced the Double Asymmetric GARCH–MIDAS model in the DCC framework.
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25

Lee, G. J., and Sun Young Hwang. "Multivariate volatility for high-frequency financial series." Korean Journal of Applied Statistics 30, no. 1 (February 28, 2017): 169–80. http://dx.doi.org/10.5351/kjas.2017.30.1.169.

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26

Chan, Felix, Christine Lim, and Michael McAleer. "Modelling multivariate international tourism demand and volatility." Tourism Management 26, no. 3 (June 2005): 459–71. http://dx.doi.org/10.1016/j.tourman.2004.02.013.

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27

Hassan, Syed Aun, and Farooq Malik. "Multivariate GARCH modeling of sector volatility transmission." Quarterly Review of Economics and Finance 47, no. 3 (July 2007): 470–80. http://dx.doi.org/10.1016/j.qref.2006.05.006.

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28

Francq, Christian, and Jean-Michel Zakoïan. "Estimating multivariate volatility models equation by equation." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 78, no. 3 (November 11, 2015): 613–35. http://dx.doi.org/10.1111/rssb.12126.

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29

Chan, David, Robert Kohn, and Chris Kirby. "Multivariate Stochastic Volatility Models with Correlated Errors." Econometric Reviews 25, no. 2-3 (September 2006): 245–74. http://dx.doi.org/10.1080/07474930600713309.

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30

Philipov, Alexander, and Mark E. Glickman. "Factor Multivariate Stochastic Volatility via Wishart Processes." Econometric Reviews 25, no. 2-3 (September 2006): 311–34. http://dx.doi.org/10.1080/07474930600713366.

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31

Gourieroux, Christian, and Razvan Sufana. "Derivative Pricing With Wishart Multivariate Stochastic Volatility." Journal of Business & Economic Statistics 28, no. 3 (July 2010): 438–51. http://dx.doi.org/10.1198/jbes.2009.08105.

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32

So, Mike K. P., and Susanna W. Y. Kwok. "A multivariate long memory stochastic volatility model." Physica A: Statistical Mechanics and its Applications 362, no. 2 (April 2006): 450–64. http://dx.doi.org/10.1016/j.physa.2005.08.078.

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33

Herwartz, Helmut, and Helmut L�tkepohl. "Multivariate volatility analysis of VW stock prices." International Journal of Intelligent Systems in Accounting, Finance & Management 9, no. 1 (March 2000): 35–54. http://dx.doi.org/10.1002/(sici)1099-1174(200003)9:1<35::aid-isaf176>3.0.co;2-v.

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34

So, Mike K. P., and C. Y. Choi. "A threshold factor multivariate stochastic volatility model." Journal of Forecasting 28, no. 8 (December 2009): 712–35. http://dx.doi.org/10.1002/for.1123.

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35

Clements, Adam, and Mark Bernard Doolan. "Combining multivariate volatility forecasts using weighted losses." Journal of Forecasting 39, no. 4 (January 26, 2020): 628–41. http://dx.doi.org/10.1002/for.2647.

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36

Zaharieva, Martina Danielova, Mark Trede, and Bernd Wilfling. "Bayesian semiparametric multivariate stochastic volatility with application." Econometric Reviews 39, no. 9 (May 19, 2020): 947–70. http://dx.doi.org/10.1080/07474938.2020.1761152.

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37

Xu, Ke-Li. "Robustifying multivariate trend tests to nonstationary volatility." Journal of Econometrics 169, no. 2 (August 2012): 147–54. http://dx.doi.org/10.1016/j.jeconom.2012.01.016.

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38

Noureldin, Diaa, Neil Shephard, and Kevin Sheppard. "Multivariate high-frequency-based volatility (HEAVY) models." Journal of Applied Econometrics 27, no. 6 (August 4, 2011): 907–33. http://dx.doi.org/10.1002/jae.1260.

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39

Allen, David E., Michael McAleer, Robert Powell, and Abhay K. Singh. "Volatility spillover and multivariate volatility impulse response analysis of GFC news events." Applied Economics 49, no. 33 (December 6, 2016): 3246–62. http://dx.doi.org/10.1080/00036846.2016.1257210.

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40

S. Andrei, Mihnea, Sujit K. Ghosh, and Jian Zou. "Dynamic Correlation Multivariate Stochastic Volatility Black-Litterman With Latent Factors." International Journal of Statistics and Probability 10, no. 2 (January 12, 2021): 1. http://dx.doi.org/10.5539/ijsp.v10n2p1.

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In finance, it is often of interest to study market volatility for portfolios that may consist of a large number of assets using multivariate stochastic volatility models. However, such models, though useful, do not usually incorporate investor views that might be available. In this paper we introduce a novel hierarchical Bayesian methodology of modeling volatility for a large portfolio of assets that incorporates investor&rsquo;s personal views of the market via the Black-Litterman (BL) model. We extend the scope and use of BL models by using it within a multivariate stochastic volatility model based on latent factors for dimensionality reduction but allows for time varying correlations. Detailed derivations of MCMC algorithm are provided with an illustration with S&amp;P500 asset returns. Moreover, sensitivity analysis for the confidence levels that the investor has in their personal views is also explored. Numerical results show that the proposed method provides flexible interpretation based on the investor&rsquo;s uncertainty in personal beliefs, and converges to the empirical sample estimate when their confidence level of the market becomes weak.
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41

Atoi, Ngozi V., and Chinedu G. Nwambeke. "Money and Foreign Exchange Markets Dynamics in Nigeria: A Multivariate GARCH Approach." Central Bank of Nigeria Journal of Applied Statistics 12, No. 1 (August 16, 2021): 109–38. http://dx.doi.org/10.33429/cjas.12121.5/6.

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This study examines money market and foreign exchange market dynamics in Nigeria by estimating the dynamic correlation and volatility spillovers between Nigeria Naira/US Dollar Bureau De Change (BDC) exchange rate and interbank call rate with data from January 2007 to August 2019. The study employs a dynamic conditional correlation form of GARCH model (DCC-GARCH) to access the nature of correlation, while an unrestricted bivariate BEKK-GARCH (1, 1) form of multivariate GARCH model is utilized to investigate shocks and volatility spillover of the rates. The estimated DCC-GARCH (1, 1) reveals that interest rate and exchange rate are dynamically linked negatively, suggesting that exchange rate (or interest rate) is inversely sensitive to interest rate (or exchange rate) in Nigeria. This result was substantiated by the estimated BEKK-GARCH(1, 1) model. Furthermore, the effects of news (shocks spillover) are bi-directional across the markets. However, volatility spillover is unidirectional, from exchange rate to interest rate, suggesting that, calming the volatility in foreign exchange market does guarantee moderation of volatility in the money market, whereas the reverse is not the case. The results underscore the growing influence of foreign exchange market in the financial space of the Nigerian economy. Thus, the study recommends that foreign exchange policies aimed at maintaining exchange rate stability should be sustained, having found exchange rate to be more effective in moderating interest rate volatility in Nigeria.
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42

Arize, Augustine C. "Determinants of Income Velocity in the United Kingdom: Multivariate Granger Causality." American Economist 37, no. 2 (October 1993): 40–45. http://dx.doi.org/10.1177/056943459303700207.

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Using cointegration and multivariate causality approach, this paper examines the determinants of income velocity in the United Kingdom over the period, 1973Q1–1990Q2. The results suggest that changes in interest rate, interest rate volatility, real exchange rate and money growth volatility provide information that helps predict future movements in income velocity.
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43

Zeng, Hongjun. "Volatility Modelling of Chinese Stock Market Monthly Return and Investor Sentiment Using Multivariate GARCH Models." International Journal of Accounting & Finance Review 5, no. 1 (June 22, 2020): 123–33. http://dx.doi.org/10.46281/ijafr.v5i1.635.

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This article examines the linkage and volatility spillover among Chinese Stock Market Monthly Return and Investor Sentiment, investigating the effect dynamic links of various investor sentiment indicators and Chinese stock market return volatility. Employing the DCC and BEKK GARCH, we find investor sentiment is to some extent linked to the yield fluctuations of the Chinese stock market, but the volatility spillover is relatively weak. In the test period (2005-2020), we observe that several indicators do not explain their linkage effects with CSI 300 index of return fluctuations and volatility spillovers well, with no indicators can reflect both of these effects. Most indicators are linkage with the CSI 300 index, especially consumer confidence index (CCI), new investor account openings last month (NIA) and the volume of transactions last month (TURN) have significant linkage effects with the CSI 300 index. We also find that only the CCI index has a one-way volatility spillover on the CSI 300 index, and the CSI 300 index has no volatility spillover on any indicator.
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44

Zeng, Hongjun. "Volatility Modelling of Chinese Stock Market Monthly Return and Investor Sentiment Using Multivariate GARCH Models." International Journal of Accounting & Finance Review 5, no. 1 (June 27, 2020): 123–33. http://dx.doi.org/10.46281/ijafr.v5i1.643.

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This article examines the linkage and volatility spillover among Chinese Stock Market Monthly Return and Investor Sentiment, investigating the effect dynamic links of various investor sentiment indicators and Chinese stock market return volatility. Employing the DCC and BEKK GARCH, we find investor sentiment is to some extent linked to the yield fluctuations of the Chinese stock market, but the volatility spillover is relatively weak. In the test period (2005-2020), we observe that several indicators do not explain their linkage effects with CSI 300 index of return fluctuations and volatility spillovers well, with no indicators can reflect both of these effects. Most indicators are linkage with the CSI 300 index, especially consumer confidence index (CCI), new investor account openings last month (NIA) and the volume of transactions last month (TURN) have significant linkage effects with the CSI 300 index. We also find that only the CCI index has a one-way volatility spillover on the CSI 300 index, and the CSI 300 index has no volatility spillover on any indicator.
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45

Esen, Halil Erturk. "Multivariate Stochastic Volatility Estimation with Sparse Grid Integration." Journal of Mathematical Finance 06, no. 01 (2016): 68–81. http://dx.doi.org/10.4236/jmf.2016.61009.

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46

Triantafyllopoulos, K. "Multivariate stochastic volatility with Bayesian dynamic linear models." Journal of Statistical Planning and Inference 138, no. 4 (April 2008): 1021–37. http://dx.doi.org/10.1016/j.jspi.2007.03.057.

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47

Rinnergschwentner, Wolfgang, Gottfried Tappeiner, and Janette Walde. "Multivariate Stochastic Volatility via Wishart Processes: A Comment." Journal of Business & Economic Statistics 30, no. 1 (January 2012): 164. http://dx.doi.org/10.1080/07350015.2012.634358.

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48

Izzeldin, Marwan, Mike G. Tsionas, and Panayotis G. Michaelides. "Multivariate stochastic volatility with large and moderate shocks." Journal of the Royal Statistical Society: Series A (Statistics in Society) 182, no. 3 (March 23, 2019): 887–917. http://dx.doi.org/10.1111/rssa.12443.

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49

Huang, Shian-Chang, Nan-Yu Wang, and Ming-Hsiang Huang. "Pricing multivariate options under stochastic volatility lévy processes." Journal of Information and Optimization Sciences 32, no. 2 (March 2011): 381–410. http://dx.doi.org/10.1080/02522667.2011.10700062.

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50

Wu, Sheng-Jhih, Sujit K. Ghosh, Yu-Cheng Ku, and Peter Bloomfield. "Dynamic correlation multivariate stochastic volatility with latent factors." Statistica Neerlandica 72, no. 1 (August 10, 2017): 48–69. http://dx.doi.org/10.1111/stan.12115.

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