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在金融时间序列分析中，广义自回归条件异方差模型（Generalized Autoregressive Conditional Heteroskedasticity，简称GARCH）是一类重要的波动性建模工具。标题中的"GARCH.rar_The Family_garch"暗示我们将探讨GARCH模型家族，这包括一系列GARCH模型的变种，用于捕捉金融数据中波动性的动态特征。 GARCH模型最初由Bollerslev（1986）提出，其基本形式是GARCH(1,1)模型，它将当前的残差平方与过去的残差平方及过去的方差相结合，来预测未来的方差。模型可以表示为： \[ \sigma_t^2 = \alpha_0 + \alpha_1 \epsilon_{t-1}^2 + \beta_1 \sigma_{t-1}^2 \] 其中，$\sigma_t^2$ 是第t时刻的方差，$\epsilon_{t-1}^2$ 是前一时刻的残差平方，$\alpha_0$、$\alpha_1$ 和 $\beta_1$ 是模型参数，分别代表常数项、残差平方的影响权重和过去方差的影响权重。 GARCH模型家族包括了多个变种，如EGARCH（Exponential GARCH）、GARCH-M（GARCH in Mean）、TARCH（Threshold GARCH）等，它们针对不同特性的金融数据进行优化。例如，EGARCH允许负的残差平方对波动性的影响，而TARCH则考虑了正负冲击对波动性不同的影响。在描述中提到的“Implement the univariate GARCH family model”，意味着我们要实现单变量的GARCH系列模型。在实际操作中，这通常涉及到以下步骤： 1. 数据预处理：导入金融时间序列数据，检查并处理缺失值和异常值。 2. 选择模型：根据数据特性，选择合适的GARCH变种。 3. 参数估计：使用最大似然法或其他方法估计模型参数。 4. 模型检验：通过残差分析（如残差图、自相关和偏自相关函数图、Q统计量等）检验模型的适配性。 5. 预测：利用估计出的模型对未来波动率进行预测。 6. 应用：预测结果可用于风险管理和投资决策。在提供的文件名"thesis_code2.R"和"thesis_code.R"中，很可能包含了实现上述过程的R语言代码。这些代码可能涵盖了数据读取、模型选择、参数估计、诊断检验和结果可视化等关键部分。通过阅读和理解这些代码，我们可以深入学习GARCH模型的实现细节，并能应用于实际的金融数据分析。 GARCH模型家族提供了一套强大的工具来描述和预测金融市场的波动性，而实现这些模型需要对金融时间序列分析有深入的理解，同时也需要掌握相应的编程技能。通过分析和运行给定的R代码，我们可以更好地掌握GARCH模型在实际问题中的应用。

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GARCH.rar （2个子文件）

thesis_code2.R 4KB

thesis_code.R 3KB

#garchSim（）和garchFit（） #omega - the constant coefficient of the variance equation, by default 1e-6; #alpha - the value or vector of autoregressive coefficients, by default 0.1, specifying a model of order 1; #beta - the value or vector of variance coefficients, by default 0.8, specifying a model of order 1; #The optional values for the linear part are: #mu - the intercept value, by default 0 (it implies that the mean = mu/(1-sum(ar))); #ar - the autoregressive ARMA coefficients, by default 0; #ma - the moving average ARMA coefficients, by default 0. getwd() source("Igarch.R") source("GarchM.R") mm=Igarch(x$log.return,include.mean=F,volcnt=F) sresi=x$log.return/mm$volatility pacf(sresi) pacf(sresi**2) mm1=garchM(x$log.return,type=2) mm=garchM(sp5,type=2) #------------------------------------------------------------------------# library(rugarch) ?rugarch ?ugarchspec ?ugarchfit #-------------------------------------------------------------------------# myspec=ugarchspec(variance.model = list(model = "fGARCH", garchOrder = c(1,1), submodel = "GARCH", external.regressors = NULL, variance.targeting =FALSE), mean.model = list(armaOrder = c(2,2), include.mean = TRUE, archm = FALSE, archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE), distribution.model = "ged") myfit=ugarchfit(myspec,data=x$log.return,solver="solnp") myfit res=residuals(myfit) sigma=sigma(myfit) fit=fitted(myfit) sres=residuals(myfit,standardize=T)#or sres=res/sigma for(ii in 1:15) print(Box.test(sres**2,ii,"Ljung")) ArchTest(sres) pred3=ugarchforecast(myfit,n.ahead=100) plot(fitted(pred3),type="l") plot(myfit) #------------------------------------------------------------------------# myspec=ugarchspec(variance.model = list(model = "iGARCH", garchOrder = c(1,1), submodel = NULL, external.regressors = NULL, variance.targeting = 0), mean.model = list(armaOrder = c(3,3), include.mean =FALSE , archm = FALSE, archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE), distribution.model = "ged") myfit1=ugarchfit(myspec,data=x$log.return,solver="solnp") myfit1 sres1=residuals(myfit1,standardize=T) for(ii in 1:30) print(Box.test(sres1,ii,"Ljung")) #-------------------------------------------------------------------------# myspec=ugarchspec(variance.model = list(model = "fGARCH", garchOrder = c(1,1), submodel = "GARCH", external.regressors = NULL, variance.targeting =0), mean.model = list(armaOrder = c(3,3), include.mean =TRUE , archm = TRUE, archpow = 2, arfima = FALSE, external.regressors = NULL, archex = FALSE), distribution.model = "ged") ##archm Whether to include ARCH volatility in the mean regression. ##archpow Indicates whether to use st.deviation (1) or variance (2) in the ARCH in mean regression. myfit2=ugarchfit(myspec,data=x$log.return,solver="solnp") myfit2 sres2=residuals(myfit2,standardize=T) for(ii in 1:30) print(Box.test(sres2,ii,"Ljung")) #-------------------------------------------------------------------------# myspec=ugarchspec(variance.model = list(model = "eGARCH", garchOrder = c(1,1), submodel = NULL, external.regressors = NULL, variance.targeting = FALSE), mean.model = list(armaOrder = c(0,0), include.mean = TRUE, archm = FALSE, archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE), distribution.model = "ged") myfit3=ugarchfit(myspec,data=x$log.return,solver="solnp") myfit3 sres3=residuals(myfit3,standardize=T) for(ii in 1:30) print(Box.test(sres3,ii,"Ljung")) ##LOG(GARCH) = -0.1623325008 + 0.1310836286*ABS(RESID(-1)/@SQRT(GARCH(-1))) - 0.0001938796244*RESID(-1)/@SQRT(GARCH(-1)) + 0.9920272489*LOG(GARCH(-1)) ##R中默认的egarch模型的形式是什么？？？ #--------------------------------------------------------------------------# myspec=ugarchspec(variance.model = list(model = "fGARCH", garchOrder = c(1,1), submodel = "TGARCH", external.regressors = NULL, variance.targeting = FALSE), mean.model = list(armaOrder = c(3,3), include.mean = TRUE, archm =FALSE, archpow = 1, arfima = FALSE, external.regressors = NULL, archex = FALSE), distribution.model = "std") myfit4=ugarchfit(myspec,data=x$log.return,solver="solnp") myfit4 sres4=residuals(myfit4,standardize=T) for(ii in 1:30) print(Box.test(sres4,ii,"Ljung"))

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