ARIMA-GARCH模型
> arimagarch.fit=garchFit(~arma(1, 2)+garch(1,1), data=capm.model$residuals, algorithm="nlminb+nm", trace=F, include.mean=F) > summary(arimagarch.fit)Title: GARCH Modelling Call: garchFit(formula = ~arma(1, 2) + garch(1, 1), data = capm.model$residuals, include.mean = F, trace = F, algorithm = "nlminb+nm") Mean and Variance Equation: data ~ arma(1, 2) + garch(1, 1)<environment: 0x0000000016430098> [data = capm.model$residuals] Conditional Distribution: norm Coefficient(s): ar1 ma1 ma2 omega alpha1 beta1 0.7056438 -0.6594565 -0.0576294 0.0015822 0.0235457 0.9700100 Std. Errors: based on Hessian Error Analysis: Estimate Std. Error t value Pr(>|t|) ar1 0.7056438 0.2662349 2.650 0.008038 ** ma1 -0.6594565 0.2674443 -2.466 0.013672 * ma2 -0.0576294 0.0292255 -1.972 0.048622 * omega 0.0015822 0.0008641 1.831 0.067094 . alpha1 0.0235457 0.0060596 3.886 0.000102 ***beta1 0.9700100 0.0078065 124.256 < 2e-16 ***---Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Log Likelihood: -901.7432 normalized: -0.7055894 Description: Sat Jan 28 01:00:06 2017 by user: hp Standardised Residuals Tests: Statistic p-Value Jarque-Bera Test R Chi^2 278.4188 0 Shapiro-Wilk Test R W 0.9833757 6.135388e-11 Ljung-Box Test R Q(10) 8.44004 0.5859366 Ljung-Box Test R Q(15) 11.05071 0.7489917 Ljung-Box Test R Q(20) 21.79654 0.3516525 Ljung-Box Test R^2 Q(10) 5.231958 0.875154 Ljung-Box Test R^2 Q(15) 8.541135 0.9002633 Ljung-Box Test R^2 Q(20) 9.225074 0.9801507 LM Arch Test R TR^2 7.184211 0.8452038 Information Criterion Statistics: AIC BIC SIC HQIC 1.420568 1.444761 1.420525 1.429653 请按照结果做个详细的解释,谢谢!

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