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DYNAMIC CONDITIONAL CORRELATION----Engle

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Abstract
Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results.
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assets considered in spite of the apparent need for bigger correlation matrices. In most cases, the number of parameters in large models is too big for easy optimization. In this paper Dynamic Conditional Correlation (DCC) estimators are proposed that have the flexibility of univariate GARCH but not the complexity of conventional multivariate GARCH. These models, which parameterize the conditional correlations directly, are naturally estimated in two steps – the first is a series of univariate GARCH estimates and the second the correlation estimate. These methods have clear computational advantages over multivariate GARCH models in that the number of parameters to be estimated in the correlation process is independent of the number of series to be correlated. Thus potentially very large correlation matrices can be estimated. In this paper, the accuracy of the correlations estimated by a variety of methods is compared in bivariate settings where many methods are feasible. An analysis of the performance of Dynamic Conditional Correlation methods for large covariance matrices is considered in Engle and Sheppard(2001). The next section of the paper will give a brief overview of various models for estimating correlations. Section 3 will introduce the new method and compare it with some of the other cited approaches. Section 4 will investigate some statistical properties of the method. Section 5 describes a Monte Carlo exon 6. Section 7 presents empirical results for several pairs of daily time series and Section 8 concludes.
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This research has been supported by NSF grant SBR-9730062 and NBER AP group. The author wishes to thank Kevin Sheppard for research assistance, and Pat Burns and John Geweke for insightful comments. Thanks also go to seminar participants at New York University, UCSD, Academica Sinica, Taiwan, CNRS Montreal, University of Iowa, Journal of Applied Econometrics Lectures, Cambridge, England, CNRS Aussois, Brown University, Fields Institute University of Toronto, and Riskmetrics.
DYNAMIC CONDITIONAL CORRELATION – A SIMPLE CLASS OF MULTIVARIATE GARCH MODELS
Robert Engle1 July 1999 Revised Jan 2002 Forthcoming Journal of Business and Economic Statistics 2002
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I.
INTRODUCTION
Correlations are critical inputs for many of the common tasks of financial management. Hedges require estimates of the correlation between the returns of the assets in the hedge. If the correlations and volatilities are changing, then the hedge ratio should be adjusted to account for the most recent information. Similarly, structured products such as rainbow options that are designed with more than one underlying asset, have prices that are sensitive to the correlation between the underlying returns. A forecast of future correlations and volatilities is the basis of any pricing formula. Asset allocation and risk assessment also rely on correlations, however in this case a large number of correlations are often required. Construction of an optimal portfolio with a set of constraints requires a forecast of the covariance matrix of the returns. Similarly, the calculation of the standard deviation of today’s portfolio requires a covariance matrix of all the assets in the portfolio. These functions entail estimation and forecasting of large covariance matrices, potentially with thousands of assets. The quest for reliable estimates of correlations between financial variables has been the motivation for countless academic articles, practitioner conferences and Wall Street research. Simple methods such as rolling historical correlations and exponential smoothing are widely used. More complex methods such as varieties of multivariate GARCH or Stochastic Volatility have been extensively investigated in the econometric literature and are used by a few sophisticated practitioners. To see some interesting applications, examine Bollerslev, Engle and Wooldridge(1988), Bollerslev(1990), Kroner and Claessens(1991), Engle and Mezrich(1996), Engle, Ng and Rothschild(1990) and surveys by Bollerslev, Chou and Kroner(1992), Bollerslev Engle and Nelson(1994), and Ding and Engle(2001). In very few of these papers are more than 5

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dcc garch 动态相关系数

dcc garch 动态相关系数

dcc garch 动态相关系数English.## DCC-GARCH: Dynamic Conditional Correlation.In financial time series analysis, it is important to model the volatility and correlation of asset returns. The dynamic conditional correlation (DCC) model, introduced by Engle (2002), is a popular choice for capturing the time-varying correlation between multiple assets. The DCC-GARCH model combines the DCC model with the generalized autoregressive conditional heteroskedasticity (GARCH) model to capture both the time-varying volatility and correlation of asset returns.Model Specification.The DCC-GARCH model is specified as follows:Mean equation:`。

R_t = \mu + \epsilon_t.`。

where:R_t is a vector of asset returns at time t.μ is a vector of mean returns.ε_t is a vector of error terms.Variance equation:`。

h_t = \omega + \alpha_1 h_{t-1} + \beta_1 ε_{t-1}^2。

航运市场与大宗商品市场动态溢出效应研究

航运市场与大宗商品市场动态溢出效应研究


16
2021年 总第313期
海运经济与管理世卿®运
证明国际经济形势良好，而BDI低于2 000,通常代 表着航运企业处于亏损状态，也表明存在经济危机 的可能。因此，通过了解BDI的波动规律并采取特
定的步骤来规避风险，船东可以避免巨额损失，而 投资者也可以了解到市场动态。图1为2010年至 2020年主要的航运指数趋势图。
（二）大宗商品市场的波动机理 大宗商品作为全球贸易的基础货物，包括能 源、金属、农产品等，都是经济建设的必需品。大 宗商品具有价格波动大、供需量大、方便运输的特 性，所交易的商品为重要的生产物资和生存物资， 是国际贸易以及建设的基石。而大宗商品也具有金 融属性，可以作为标的物进行交易，如石油、金 属、农产品、化工材料等。常见的大宗商品市场的 交易对象主要包括农副产品、金属产品以及能源 （如原油）等。 造成大宗商品波动的因素有很多，可以分为供
品市场间波动溢出的联动性与时变性进行实证研究。研究表明，航运市场与大宗商品市场存在持续性较强的动态相关性， 航运指数BDI与CRB商品指数和WTI原油期货指数都有一定的动态相关性。在2011年叙利亚战争、2014年2月埃博拉病毒
爆发、2015年原油暴跌以及2020年新冠疫情全球蔓延等重大事件发生期间，航运市场与大宗商品市场的动态相关系数都出
海运经济与管理世摺!®运
航运市场与大宗商品市场 动态溢出效应研究*
孟斌周昱彤匡海波
摘要：航运是大宗商品的主要运输手段，航运市场作为连通全球供应链的纽带，在国际贸易中占据重要地位。选取BDI 指数、CRB商品指数、WTI原油期货指数等衡量航运和大宗商品市场，通过构建DCC-GARCH模型对航运市场与大宗商
（三）市场间的溢出效应机理 分析航运市场与大宗商品市场的波动机理，可 以发现航运市场与大宗商品市场间存在着紧密的关 系，包括直接联系、间接联系以及共同受到重大事 件影响，即航运市场与大宗商品市场间溢出效应的 产生机理。 1. 航运市场与大宗商品市场的直接联系 航运市场的主要运输对象是干散货和液体散 货，包括粮食、金属矿石、原油等，均是维持世界 经济运转的基本原料，而这些货物也大多属于大宗 商品的范畴，这就形成了航运市场与大宗商品市场 间的最直接联系。航运是大宗商品市场的运输手 段，大宗商品是航运的运输对象，自然而然航运市 场与大宗商品市场间会存在着联动关系。 2. 航运市场与大宗商品市场的间接联系 航运在运输货物的过程中使用的燃料油的价格 会影响船舶运行的成本从而影响运价，而燃料油的 原料为石油，因此石油价格可以间接地从燃料角度 影响航运市场。而石油作为重要的大宗商品，在大 宗商品市场占据重要地位，从石油角度，航运市场 与大宗商品市场间也存在着紧密联系。
r语言 dcc导出条件相关系数 -回复

r语言 dcc导出条件相关系数 -回复

r语言dcc导出条件相关系数-回复R语言中的DCC模型（Dynamic Conditional Correlation Model）是一种用于估计条件相关系数的统计模型。

条件相关系数是衡量不同变量之间相关性水平的指标，它反映了变量之间的关联程度，对于金融领域中的资产组合管理、风险控制和投资决策具有重要意义。

在这篇文章中，我将详细介绍如何在R语言中使用DCC模型导出条件相关系数。

首先，我们需要安装并加载"rmgarch"包，它是一个用于金融时间序列建模和预测的R包。

你可以使用下面的代码安装该包：Rinstall.packages("rmgarch")library(rmgarch)接下来，我们需要准备数据。

DCC模型需要一个时间序列数据集，其中包含多个变量的观测值。

假设我们有一个包含三个变量（A、B和C）的数据集，可以使用以下代码加载数据：Rdata <- read.csv("data.csv")我们可以使用以下代码查看数据集的结构和前几行观测值：Rstr(data)head(data)接下来，我们需要创建一个rmgarch对象来拟合DCC模型。

我们可以使用以下代码来创建对象：Rspec <- dccspec(uspec = multispec(replicate(3,ugarchspec(variance.model = list(model = "sGARCH")), simplify = FALSE)), dccOrder = c(1, 1), distribution = "mvnorm")在上述代码中，我们使用了multispec函数来创建一个包含三个同质的GARCH模型的列表，每个模型用于估计单个变量的方差。

我们将这个列表作为参数传递给dccspec函数来创建一个多变量GARCH模型。

DCC模型与GARCH-MIDAS特性的R包说明书

DCC模型与GARCH-MIDAS特性的R包说明书

Package‘dccmidas’October13,2022Type PackageTitle DCC Models with GARCH-MIDAS Specifications in the UnivariateStepVersion0.1.0Description Estimates a variety of Dynamic Conditional Correlation(DCC)models.More in de-tail,the'dccmidas'package allows the estimation of the cor-rected DCC(cDCC)of Aielli(2013)<doi:10.1080/07350015.2013.771027>,the DCC-MIDAS of Colacito et al.(2011)<doi:10.1016/j.jeconom.2011.02.013>,the Asymmet-ric DCC of Cappiello et al.<doi:10.1093/jjfinec/nbl005>,and the Dynamic Equicorrela-tion(DECO)of Engle and Kelly(2012)<doi:10.1080/07350015.2011.652048>.'dccmidas'of-fers the possibility of including standard GARCH<doi:10.1016/0304-4076(86)90063-1>,GARCH-MIDAS<doi:10.1162/REST_a_00300>and Double Asymmetric GARCH-MIDAS<doi:10.1016/j.econmod.2018.07.025>models in the univariate estimation.Fi-nally,the package calculates also the var-cov matrix under two non-parametric models:the Mov-ing Covariance and the RiskMetrics specifications.License GPL-3LinkingTo Rcpp,RcppArmadilloEncoding UTF-8LazyData trueRoxygenNote7.1.1RdMacros RdpackDepends R(>=4.0.0)Imports Rcpp(>=1.0.5),maxLik(>=1.3-8),rumidas(>=0.1.1),rugarch(>=1.4-4),roll(>=1.1.4),xts(>=0.12.0),tseries(>=0.10.47),Rdpack(>=1.0.0),lubridate(>=1.7.9),zoo(>=1.8.8),stats(>=4.0.2),utils(>=4.0.2)Suggests knitr,rmarkdownNeedsCompilation yesAuthor Vincenzo Candila[aut,cre]Maintainer Vincenzo Candila<****************************>Repository CRANDate/Publication2021-03-1510:00:07UTC12cov_eval R topics documented:cov_eval (2)dcc_fit (3)Det (7)ftse100 (7)indpro (8)Inv (9)nasdaq (9)plot_dccmidas (10)sp500 (11)Index13 cov_eval Var-cov matrix evaluationDescriptionEvaluates the estimated var-cov matrix H_t with respect to a covariance proxy,under different robust loss functions(Laurent et al.2013).The losses considered are also used in Amendola et al.(2020).Usagecov_eval(H_t,cov_proxy=NULL,r_t=NULL,loss="FROB")ArgumentsH_t Estimated covariance matrix,formatted as arraycov_proxy optional Covariance matrix,formatted as arrayr_t optional List of daily returns used to calculate H_t.If parameter’cov_proxy’is not provided,then r_t must be included.In this case,a(noise)proxy will beautomatically usedloss Robust loss function to use.Valid choices are:"FROB"for Frobenius(by de-fault),"SFROB"for Squared Frobenius,"EUCL"for Euclidean,"QLIKE"forQLIKE and"RMSE"for Root Mean Squared ErrorsValueThe value of the loss for each tReferencesAmendola A,Braione M,Candila V,Storti G(2020).“A Model Confidence Set approach to the combination of multivariate volatility forecasts.”International Journal of Forecasting,36(3),873-891.doi:10.1016/j.ijforecast.2019.10.001.Laurent S,Rombouts JV,Violante F(2013).“On loss functions and ranking forecasting perfor-mances of multivariate volatility models.”Journal of Econometrics,173(1),1–10.doi:10.1016/ j.jeconom.2012.08.004.Examplesrequire(xts)#open to close daily log-returnsr_t_s<-log(sp500[ 2010/2019 ][,3])-log(sp500[ 2010/2019 ][,1])r_t_n<-log(nasdaq[ 2010/2019 ][,3])-log(nasdaq[ 2010/2019 ][,1])r_t_f<-log(ftse100[ 2010/2019 ][,3])-log(ftse100[ 2010/2019 ][,1])db_m<-merge.xts(r_t_s,r_t_n,r_t_f)db_m<-db_m[complete.cases(db_m),]colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")#list of returnsr_t<-list(db_m[,1],db_m[,2],db_m[,3])#estimationK_c<-144N_c<-36cdcc_est<-dcc_fit(r_t,univ_model="sGARCH",distribution="norm",corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)cov_eval(cdcc_est$H_t,r_t=r_t)[(K_c+1):dim(cdcc_est$H_t)[3]]dcc_fit DCCfit(first and second steps)DescriptionObtains the estimation of a variety of DCC models,using as univariate models both GARCH and GARCH-MIDAS specifications.Usagedcc_fit(r_t,univ_model="sGARCH",distribution="norm",MV=NULL,K=NULL,corr_model="cDCC",lag_fun="Beta",N_c=NULL,K_c=NULL)Argumentsr_t List of daily returns on which estimate a DCC model.Each daily return must bean’xts’object.Note that the sample period of the returns should be the same.Otherwise,a merge is performeduniv_model Specification of the univariate model.Valid choices are:some of the specifica-tions used in the rugarch(ugarchspec)and rumidas(ugmfit)packages.Morein detail,the models coming from rugarch are:model Valid models(currentlyimplemented)are’sGARCH’,’eGARCH’,’gjrGARCH’,’iGARCH’,and’cs-GARCH’.The models implemented from rumidas are:’GM_skew’,’GM_noskew’,’DAGM_skew’,and’DAGM_noskew’distribution optional Distribution chosen for the univariate estimation.Valid choices are:"norm"(by default)and"std",respectively,for the Normal and Student’s t dis-tributionsMV optional MIDAS variable to include in the univariate estimation,if the modelspecificied is a GARCH-MIDAS(GM,Engle et al.(2013))or a Double Asym-metric GM(DAGM,Engle et al.(2013)).In the case of MIDAS-based models,please provide a list of the MIDAS variables obtained from the mv_into_matfunction.If the same MV variable is used,then provide always a list,with thesame(transformed)variable repeatedK optional The number of lagged realization of MV variable to use,if’univ_model’has a MIDAS termcorr_model Correlation model used.Valid choices are:"cDCC"(the corrected DCC ofAielli(2013)),"aDCC"(the asymmetric DCC model of Cappiello et al.(2006)),"DECO"(Dynamic equicorrelation of Engle and Kelly(2012)),and"DCCMI-DAS"(the DCC-MIDAS of Colacito et al.(2011)).By detault,it is"cDCC"lag_fun g function to use.Valid choices are"Beta"(by default)and"Al-mon",for the Beta and Exponential Almon lag functions,respectively,if’univ_model’has a MIDAS term and/or if’corr_model’is"DCCMIDAS"N_c optional Number of(lagged)realizations to use for the standarized residualsforming the long-run correlation,if’corr_model’is"DCCMIDAS"K_c optional Number of(lagged)realizations to use for the long-run correlation,if’corr_model’is"DCCMIDAS"DetailsFunction dcc_fit implements the two-steps estimation of the DCC models.In thefirst step,a variety of univariate models are considered.These models can be selected using for the pa-rameter’univ_model’one of the following choices:’sGARCH’(standard GARCH of Bollerslev (1986)),’eGARCH’of Nelson(1991),’gjrGARCH’of Glosten et al.(1993),’iGARCH’(Integrated GARCH of Engle and Bollerslev(1986)),’csGARCH’(the Component GARCH of Engle and Lee (1999)),’GM_noskew’and’GM_skew’(the GARCH-MIDAS model of Engle et al.(2013),respec-tively,without and with the asymmetric term in the short-run component),and’DAGM_noskew’and’DAGM_skew’(the Double Asymmetric GARCH-MIDAS model of Amendola et al.(2019), respectively,without and with the asymmetric term in the short-run component).Valuedcc_fit returns an object of class’dccmidas’.The function summary.dccmidas can be used to print a summary of the results.Moreover,an object of class’dccmidas’is a list containing the following components:•assets:Names of the assets considered.•model:Univariate model used in thefirst step.•est_univ_model:List of matrixes of estimated coefficients of the univariate model,with the QML(Bollerslev and Wooldridge1992)standard errors.•corr_coef_mat:Matrix of estimated coefficients of the correlation model,with the QML stan-dard errors.•mult_model:Correlation model used in the second step.•obs:The number of daily observations used for the estimation.•period:The period of the estimation.•H_t:Conditional covariance matrix,reported as an array.•R_t:Conditional correlation matrix,reported as an array.•R_t_bar:Conditional long-run correlation matrix,reported as an array,if the correlation ma-trix includes a MIDAS specification.•est_time:Time of estimation.•Days:Days of the sample period.•llk:The value of the log-likelihood(for the second step)at the maximum.ReferencesAielli GP(2013).“Dynamic conditional correlation:on properties and estimation.”Journal of Business&Economic Statistics,31(3),282–299.doi:10.1080/07350015.2013.771027.Amendola A,Candila V,Gallo GM(2019).“On the asymmetric impact of macro–variables on volatility.”Economic Modelling,76,135–152.doi:10.1016/j.econmod.2018.07.025.Bollerslev T(1986).“Generalized autoregressive conditional heteroskedasticity.”Journal of Econo-metrics,31(3),307–327.doi:10.1016/03044076(86)900631.Bollerslev T,Wooldridge JM(1992).“Quasi-maximum likelihood estimation and inference in dy-namic models with time-varying covariances.”Econometric Reviews,11,143–172.doi:10.1080/ 07474939208800229.Cappiello L,Engle RF,Sheppard K(2006).“Asymmetric dynamics in the correlations of global equity and bond returns.”Journal of Financial Econometrics,4(4),537–572.doi:10.1093/jjfinec/ nbl005.Colacito R,Engle RF,Ghysels E(2011).“A component model for dynamic correlations.”Journalof Econometrics,164(1),45–59.doi:10.1016/j.jeconom.2011.02.013.Engle R,Kelly B(2012).“Dynamic equicorrelation.”Journal of Business&Economic Statis-tics,30(2),212–228.doi:10.1080/07350015.2011.652048.Engle RF,Bollerslev T(1986).“Modelling the persistence of conditional variances.”Econometric Reviews,5(1),1–50.doi:10.1080/07474938608800095.Engle RF,Ghysels E,Sohn B(2013).“Stock market volatility and macroeconomic fundamen-tals.”Review of Economics and Statistics,95(3),776–797.doi:10.1162/REST_a_00300.Engle RF,Lee GJ(1999).“A Long-run and Short-run Component Model of Stock Return V olatil-ity.”In Engle RF,White H(eds.),Cointegration,Causality,and Forecasting:A Festschrift in Honor of Clive W.J.Granger,475–497.Oxford University Press,Oxford.Glosten LR,Jagannathan R,Runkle DE(1993).“On the relation between the expected value and the volatility of the nominal excess return on stocks.”The Journal of Finance,48(5),1779–1801.doi:10.1111/j.15406261.1993.tb05128.x.Nelson DB(1991).“Conditional heteroskedasticity in asset returns:A new approach.”Econo-metrica,59,347–370.doi:10.2307/2938260.Examplesrequire(xts)#open to close daily log-returnsr_t_s<-log(sp500[ 2005/2008 ][,3])-log(sp500[ 2005/2008 ][,1])r_t_n<-log(nasdaq[ 2005/2008 ][,3])-log(nasdaq[ 2005/2008 ][,1])r_t_f<-log(ftse100[ 2005/2008 ][,3])-log(ftse100[ 2005/2008 ][,1])db_m<-merge.xts(r_t_s,r_t_n,r_t_f)db_m<-db_m[complete.cases(db_m),]colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")#list of returnsr_t<-list(db_m[,1],db_m[,2],db_m[,3])#MV transformation(same MV for all the stocks)require(rumidas)mv_m<-mv_into_mat(r_t[[1]],diff(indpro),K=12,"monthly")#list of MVMV<-list(mv_m,mv_m,mv_m)#estimationK_c<-144N_c<-36dccmidas_est<-dcc_fit(r_t,univ_model="GM_noskew",distribution="norm",MV=MV,K=12,corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)dccmidas_estsummary.dccmidas(dccmidas_est)Det7 Det Matrix determinantDescriptionCalculates the determinant of a numeric matrix.UsageDet(x)Argumentsx a numeric matrixValueThe determinant of x.Examplesx<-matrix(sample(1:25,25,replace=TRUE),ncol=5)Det(x)ftse100FTSE100dataDescriptionDaily data on FTSE100collected from the realized library of the Oxford-Man Institute(Heber et al.2009).Usagedata(ftse100)FormatAn object of class"xts".Detailsftse100includes the open price(open_price),the realized variance(rv5),and the close price(close_price).The realized variance has been calculated using intradaily intervals offive minutes(Andersen and Bollerslev1998).8indproSourceRealized library of the Oxford-Man InstituteReferencesAndersen TG,Bollerslev T(1998).“Answering the Skeptics:Yes,Standard V olatility Models do Provide Accurate Forecasts.”International Economic Review,39,885–905.doi:10.2307/2527343.Heber G,Lunde A,Shephard N,Sheppard K(2009).“OMI’s realised library,version0.1.”Oxford–Man Institute,University of Oxford.Exampleshead(ftse100)summary(ftse100)indpro Monthly U.S.Industrial ProductionDescriptionMonthly data on the U.S.Industrial Production index(IP,index2012=100,seasonally adjusted) collected from the Federal Reserve Economic Data(FRED)archive.The IP has been used as MIDAS term in different contributions(see,for instance,Engle et al.(2013),Conrad and Loch (2015),and Amendola et al.(2017)).Usagedata(indpro)FormatAn object of class"xts".SourceArchive of the Federal Reserve Economic Data(FRED)ReferencesAmendola A,Candila V,Scognamillo A(2017).“On the influence of US monetary policy on crude oil price volatility.”Empirical Economics,52(1),155–178.doi:10.1007/s0018101610695.Conrad C,Loch K(2015).“Anticipating Long-Term Stock Market V olatility.”Journal of Applied Econometrics,30(7),1090–1114.doi:10.1002/jae.2404.Engle RF,Ghysels E,Sohn B(2013).“Stock market volatility and macroeconomic fundamentals.”Review of Economics and Statistics,95(3),776–797.doi:10.1162/REST_a_00300.Inv9Exampleshead(indpro)summary(indpro)plot(indpro)Inv Inverse of a matrixDescriptionCalculates the inverse of a numeric matrixUsageInv(x)Argumentsx a numeric matrixValueThe inverse of x.Examplesx<-matrix(sample(1:25,25,replace=TRUE),ncol=5)Inv(x)nasdaq NASDAQ dataDescriptionDaily data on NASDAQ collected from the realized library of the Oxford-Man Institute(Heber et al.2009).Usagedata(nasdaq)FormatAn object of class"xts".10plot_dccmidas Detailsnasdaq includes the open price(open_price),the realized variance(rv5),and the close price(close_price).The realized variance has been calculated using intradaily intervals offive minutes(Andersen and Bollerslev1998).SourceRealized library of the Oxford-Man InstituteReferencesAndersen TG,Bollerslev T(1998).“Answering the Skeptics:Yes,Standard V olatility Models do Provide Accurate Forecasts.”International Economic Review,39,885–905.doi:10.2307/2527343.Heber G,Lunde A,Shephard N,Sheppard K(2009).“OMI’s realised library,version0.1.”Oxford–Man Institute,University of Oxford.Exampleshead(nasdaq)summary(nasdaq)plot_dccmidas Plot method for’dccmidas’classDescriptionPlots of the conditional volatilities on the main diagonal and of the conditional correlations on the extra-diagonal elements.Usageplot_dccmidas(x,K_c=NULL,vol_col="black",long_run_col="red",cex_axis=0.75,LWD=2,asset_sub=NULL)sp50011Argumentsx An object of class’dccmidas’,that is the result of a call to dcc_fit.K_c optional Number of(lagged)realizations to use for the long-run correlation,,if ’corr_model’is"DCCMIDAS"vol_col optional Color of the volatility and correlation plots."black"by defaultlong_run_col optional Color of the long-run correlation plots,if present."red"by default cex_axis optional Size of the x-axis.Default to0.75LWD optional Width of the plotted lines.Default to2asset_sub optional Numeric vector of selected assets to consider for the plot.NULL by defaultValueNo return value,called for side effectsExamplesrequire(xts)#open to close daily log-returnsr_t_s<-log(sp500[ 2010/2019 ][,3])-log(sp500[ 2010/2019 ][,1])r_t_n<-log(nasdaq[ 2010/2019 ][,3])-log(nasdaq[ 2010/2019 ][,1])r_t_f<-log(ftse100[ 2010/2019 ][,3])-log(ftse100[ 2010/2019 ][,1])db_m<-merge.xts(r_t_s,r_t_n,r_t_f)db_m<-db_m[complete.cases(db_m),]colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")#list of returnsr_t<-list(db_m[,1],db_m[,2],db_m[,3])#estimationK_c<-144N_c<-36cdcc_est<-dcc_fit(r_t,univ_model="sGARCH",distribution="norm",corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)plot_dccmidas(cdcc_est,K_c=144)sp500S&P500dataDescriptionDaily data on S&P500collected from the realized library of the Oxford-Man Institute(Heber et al.2009).Usagedata(sp500)12sp500FormatAn object of class"xts".Detailssp500includes the open price(open_price),the realized variance(rv5),and the close price(close_price).The realized variance has been calculated using intradaily intervals offive minutes(Andersen and Bollerslev1998).SourceRealized library of the Oxford-Man InstituteReferencesAndersen TG,Bollerslev T(1998).“Answering the Skeptics:Yes,Standard V olatility Models do Provide Accurate Forecasts.”International Economic Review,39,885–905.doi:10.2307/2527343.Heber G,Lunde A,Shephard N,Sheppard K(2009).“OMI’s realised library,version0.1.”Oxford–Man Institute,University of Oxford.Exampleshead(sp500)summary(sp500)Index∗datasetsftse100,7indpro,8nasdaq,9sp500,11cov_eval,2dcc_fit,3,11Det,7ftse100,7indpro,8Inv,9mv_into_mat,4nasdaq,9plot_dccmidas,10sp500,11summary.dccmidas,5ugarchspec,4ugmfit,413。