Answer Happy

Please read the following R scripts for the analysis of S&P 500 returns and answer questions from 15 to 20. > sp5=scan("sp500.txt") Read 792 items > pacf(sp5) >ml=garchFit(~arma(3,0)+garch(1,1),data=sp5,trace=F) > summary(ml) Title: GARCH Modelling Call: garchFit(formula = ~arma(3,0)+garch(1, 1), data = sp5, trace = F) = = Mean and Variance Equation: data ~ arma(3, 0) + garch(1, 1) [data = sp5] Conditional Distribution: norm Error Analysis: Estimate mu 7.708e-03 ar1 3.197e-02 ar2 -3.026e-02 ar3 -1.065e-02 omega 7.975e-05 alphal 1.242e-01 betal 8.530e-01 Std. Error 1.607e-03 3.837e-02 3.841e-02 3.756e-02 2.810e-05 2.247e-02 2.183e-02 t value 4.798 0.833 -0.788 -0.284 2.838 5.529 39.075 10 Pr(>It) 1.6le-06 *** 0.40473 0.43076 0.77677 0.00454 ** 3.22e-08 *** < 2e-16 *** Log Likelihood: 1272.179 normalized: 1.606287

Standardised Residuals Tests: 17. Does the standardized residual & follow the assumed conditional normal distribution at 5% significance level? a. yes b.no c.not sure Jarque-Bera Test Shapiro-Wilk Test Ljung-Box Test Ljung-Box Test Ljung-Box Test Ljung-Box Test Ljung-Box Test Ljung-Box Test LM Arch Test Statistic R Chi^2 73.04842 R R W 0.985797 R Q(10) 11.56744 R R Q(15) 17.78747 RQ(20) 24.11916 R2 (10) 10.31614 R 2 0/15) 14.22819 R-2 0(20) 16.79404 R TR*2 13.34305 p-Value I.1 10223e-16 5.9619940-07 0.315048 0.2740039 0.2372256 0.4132089 0.5082978 0.6663038 0.3446175 18. Are the autocorrelations of first 15 lags of the standardized residuals jointly zero at 5% significance level? a. yes b. no c.not sure Information Criterion Statistics: AIC BIC HQIC -3.194897 3.153581 3.195051 3.179018 SIC 19. Is there ARCH effect in the standardized residuals at 5% significance level? > predict(m2,6) mcanForccast micanError standardDeviation 1 0.0617449721 0.05377242 0.05377242 2 0.007449721 0.05388567 0.05388567 3 0.007449721 0.0539201 0.05399601 4 4 0.007449721 0.05410353 0.05410353 5 0.007449721 0.05420829 0.05420829 6 0.007449721 0.05431038 0.05431038 b. no c. not sure 1. 20. Which is the 3-step ahcad forecast for conditional variance ? a. 0.007449721 ht. 0.0074497212 c. 0.5399601 d 0.53996012 15. For the estimated model (ml in the R scripts), we could write the model as ro = 4, + 4+2-1+, 12-2+2-3 +0,4 = 0,2, 0 = +0,0 +02. Which of the following is -1 false for the estimated coefficients? il (= 0.007708 b. 0.1242 C B = 0.853 d. 0.03197 c. = -0.03026 16. For the estimated model (ml in the R scripts) as written in question 15, which of the parameter estimates isfarc insignificant different from zero at 5% significance level? ܕ܀܀.ܕ .6 c. d. A hath aandid e.