SARIMA(1,1,1)(0,1,2)[12]-GARCH(1,1)模型拟合代码（R语言）

以下是使用R语言中的forecast和rugarch库实现SARIMA(1,1,1)(0,1,2)[12]-GARCH(1,1)模型拟合的代码：

library(forecast)
library(rugarch)

# 读取数据
data <- read.csv("data.csv", header=TRUE, sep=",")
data.ts <- ts(data$Value, start=c(2010, 1), frequency=12)

# 拟合SARIMA模型
sarima_order <- c(1,1,1)
sarima_seasonal_order <- c(0,1,2)
sarima_model <- arima(data.ts, order=sarima_order, seasonal=sarima_seasonal_order)
sarima_residuals <- residuals(sarima_model)

# 检验SARIMA模型残差
sarima_ljungbox <- Box.test(sarima_residuals, lag=20, type="Ljung-Box")
sarima_pvalue <- sarima_ljungbox$p.value
print(paste("Ljung-Box test (SARIMA): p-value=", round(sarima_pvalue, 4)))

# 拟合GARCH模型
garch_spec <- ugarchspec(mean.model=list(armaOrder=c(0,0)), variance.model=list(garchOrder=c(1,1)))
garch_model <- ugarchfit(garch_spec, sarima_residuals)
garch_residuals <- residuals(garch_model)

# 检验GARCH模型残差
garch_ljungbox <- Box.test(garch_residuals, lag=20, type="Ljung-Box")
garch_pvalue <- garch_ljungbox$p.value
print(paste("Ljung-Box test (GARCH): p-value=", round(garch_pvalue, 4)))

# 绘制SARIMA-GARCH模型的拟合结果
sarima_forecast <- forecast(sarima_model, h=12)
garch_forecast <- ugarchforecast(garch_model, n.ahead=12)
garch_std <- sqrt(garch_forecast@forecast$varianceForecast)
garch_upper <- sarima_forecast$upper + 1.96 * garch_std
garch_lower <- sarima_forecast$lower - 1.96 * garch_std
plot(data.ts, type="l")
lines(sarima_forecast$mean, col="blue")
lines(sarima_forecast$upper, col="blue", lty=2)
lines(sarima_forecast$lower, col="blue", lty=2)
lines(sarima_forecast$mean + garch_forecast@forecast$meanForecast, col="red")
lines(garch_upper, col="red", lty=2)
lines(garch_lower, col="red", lty=2)
title("SARIMA-GARCH Fitting")
legend("topleft", c("SARIMA", "SARIMA-GARCH"), lty=c(1,1), col=c("blue","red"))

# 预测未来数据
sarima_forecast <- forecast(sarima_model, h=12)
garch_forecast <- ugarchforecast(garch_model, n.ahead=12)
garch_std <- sqrt(garch_forecast@forecast$varianceForecast)
garch_upper <- sarima_forecast$upper + 1.96 * garch_std
garch_lower <- sarima_forecast$lower - 1.96 * garch_std
plot(data.ts, type="l")
lines(sarima_forecast$mean, col="blue")
lines(garch_forecast@forecast$meanForecast, col="red")
lines(garch_upper, col="red", lty=2)
lines(garch_lower, col="red", lty=2)
title("SARIMA-GARCH Forecast")
legend("topleft", c("SARIMA", "SARIMA-GARCH"), lty=c(1,1), col=c("blue","red"))

在上述代码中，我们首先读取了时间序列数据并将其转换为R中的ts对象。然后，我们使用arima函数拟合SARIMA模型，并使用ugarchspec和ugarchfit函数拟合GARCH模型。之后，我们分别使用Box.test函数检验了SARIMA和GARCH模型的残差。最后，我们使用forecast函数预测未来数据，并绘制了预测结果。需要注意的是，在R中实现SARIMA-GARCH模型需要先安装forecast和rugarch库。